Simulation of Rolling Mill to Computeand Improve Load Distribution

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Simulation of Rolling Mill to Compute and Improve Load Distribution

Pontus Darth

Mechanical Engineering, master's level 2021

Luleå University of Technology

Department of Engineering Sciences and Mathematics

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Preface

This master thesis marks the end of the masters of science program, mechanical engineering at the Luleå University of Technology. The purpose of this project was to create a parametric ﬁnite element model of SSAB Borlänges hot rolling mill to simulate and improve the load distribution between the rolls i order to prevent roll spalling problems. This project was done at Swerim AB’s research facility in Luleå in cooperation with SSAB and the Luleå University of Technology.

This project would not have been possible without the help of many people, therefor i would like to send my thanks to:

Patrik Sidestam, research engineer at the department of heat and processing of Swerim and supervisor for this project for excellent guidance, important inputs and interesting discussions.

Andreas Lundbäck, associate professor at the division of solid mechanics at the technical university of Luleå.

For providing guidance and essential support regarding modelling and simulations.

Emil Gren and Mats Thurgren of SSAB for sharing their vast knowledge of rolling mills and providing data and necessary information.

My girlfriend and partner in crime Maja Stenström, my brother David, my sister Anna, my parents Mikael and Agneta Darth, and many others for providing emotional support throughout my education.

Since parting is such sweet sorrow, i have to say that will miss my university. I will miss the many people i have met and grown to love these past years. I will forever be thankful for the opportunity and the experience of being a student of the Luleå University of Technology.

- Pontus Darth

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Abstract

This master thesis was done at Swerim AB in cooperation with SSAB and the Technical University of Luleå in the purpose of preventing spalling problem in hot rolling mills. Spallings are a fatigue damage that occurs on the rolls due to extreme loads and unfavorable conditions between the rolls in a mill.

This report describes how the roughing mill, which is the ﬁrst of a series of hot rolling mills is modelled and simulated in order to compute the load distribution between the rolls. The load distribution tells a lot where the spalling problems occurs.

By computer aided design and simulations with the ﬁnite element method a parametric computational model was created and used to simulate the load distribution between the work roll and backup roll with worn and fresh rolls. These simulations showed what the load distribution looks like when using new rolls and that the load distribution is especially bad when the work roll is worn.

The computational model was used to simulate how the load distribution changes with diﬀerent geometries on the backup roll to provide valuable input and suggest new designs on the backup roll currently used by SSAB Borlänge.

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1 Introduction

Since the middle age, the steel industry have been a solid pillar of Swedish economics. With a solid reputation as the makers of the best iron and steel in the world. During the middle age Sweden mostly exported raw iron in the form of half round objects that were split in the middle called osmunds and later bar iron. Throughout the history the iron industry in Sweden focused more and more on refining the raw iron by forging it to steal, slowly reducing the export of raw iron and increasing the export of refined steal products. Nowadays, steel made in Sweden is still regarded as the best in the world and as Jernkontoret (2020) states in the article Världsledande stålföretag (World leading steel companies). Sweden has world leading companies in high strength and high tech steel and steel products with research institutes such as Swerim AB which specializes in research in metallurgy and production of different metals and alloys. Swerim is owned by the industry with a many member companies that uses hot rolling mills to produce sheet steel. This is why it is important for Swerim to develope methods for simulating rolling mills and provide solutions for problems that can occur in them.

This master thesis was conducted at Swerim AB, Luleå with cooperation with Luleå University of Technology and SSAB in the purpose of prevent roll spalling problems in SSAB’s hot roll mill located in Borlänge, Sweden.

1.1 Problem description

The hot rolling mill in Borlänge uses a reheating furnace to heat molded steal slabs from SSAB Luleå and then pass it through a series of rolling mills to make sheet steel. The ﬁrst rolling mill is called the roughing mill which is used to decrease most of the thickness in the slab and close any remaining cavities in the slab as shown in Figure 1. As shown in Högskolan Dalarna (2012), the rouging mill reduces the thickness in a steel slab from 22 cm to about 3 in ﬁve passes. The widths of these slabs varies from 700 to 1600 mm and approximatly 10 meters in length according to Mats Thurgren and Emil Gren, (personal communication, Mars 31, 2021)

Figure 1: Illustration of the roughing mill.

The roughing mill in Borlänge is as Schröder (2003) describes it, a Quarto mill. The quarto mill has dual roller pairs, one pair (the upper pair) located above the workpiece or slab as it is called, and one pair (the lower pair) located under the workpiece. The rolls are mounted to a mill stand as shown in Figure 2.

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Figure 2: Basic illustration of rolling mill.

The mill stand has the ability to move the rollers up and down individually. This mill uses dual pairs of rollers over and under the slab, the rolls closest to the slab is called work roll and the ones pressing on the work roll is called backup rolls. During operation, the backup roll is used to press down on the work roll to decrease bending of the work roll and generate as ﬂat sheets of steel as possible. The backup roll is needed because even though the substantial diameter of the work roll, it would still bend if the backup roll was not used, illustrated in Figure 3 below.

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the rolls in SSAB’s mill repeatedly survives campaigns of up to 60 hours under high loads, milling kilometers of steal. The high load and small contact area between the work roll and the backup roll creates large stresses in the material. Combining the huge peak stresses with cyclic load and the rolls experience the perfect recipe for material fatigue. Lund (2000) states that fatigue failures starts as micro fractures around small geometrical defects the component. The fracture then propagates and causes diﬀerent failures depending on geometry, size, and material properties. In rolling mills a common failure is roll-spalling. Due to the diﬀerent hardness in the cross section of the roll and high pressure, steal shards break away, leaving pits in the material behind as shown in Figures 4.

Figure 4: Spallings in work roll to the left and backup roll to the right, Picture curtesy of Swerim AB.

Roll spalling failures results in damaged rolls and also could damage the workpiece. The damaged roll pair needs to be changed which causes a stop in production which can be directly translated to loss of income. The rolls are also expensive, according to the rolling mill guru Mats Thurgren (personal communication, January 27, 2021), a roll costs about 1.5 million SEK and has a lifespan of 5 years. Recently the rolls in SSAB Borlänges roughing mill has failed sooner than expected, which have caused SSAB to change the roll design. They now want to know how this aﬀects the load distribution between the backup and work roll.

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1.2 Goals

The goal is to create a parametric ﬁnite element model use it to compute the load distribution during operation for the following cases to identify the the load distribution and see how a worn work roll aﬀects it.

• New work roll and backup roll.

• Worn work roll and new backup roll.

The parametricized model was then to be used to adjust the geometry on the backup roll to see if and how a better load distribution could be achieved. These test should give valuable on future roll design.

1.3 Limitations

As the rolls in the roughing mills are the objects of interest the eﬀort will be focused on simulating the action of the roughing mill. The steel slab will have to be included in the simulations to get the correct load distribution between the slab and the work roll. The focus will lie on the work roll and backup roll which is why a an advanced model of the slab wont be needed. As data was only supplied for a slabs thickness reduction from 60 to 30 mm, only this part of the roughing process can be simulated.

Measurements that deﬁnes the geometry of the worn rolls are measured when thy are outside of the mill.

Thus meaning that they are cooler when the wear is measured. The geometry of the rolls changes with the temperature of the rolls, However the change in geometry is very small. Considering the mass of the rolls and that the rolls the rolls are heated and cooled simultaneously over a long time interval it is impossible to know the distribution of temperature in the rolls without doing extensive research. Doing a extensive thermo mechanical study is outside the scope of this work.

As the rolls are the object of interest the mill stand and control rig will be excluded from the simulations.

No economical aspect will be investigated in this project as it is implied that a more durable rolls reduces costs in maintenance, scrapped material and stops in the production.

SSAB has supplied drafts of the rolls as well as necessary data in the form of measurements and important information. With respect to SSAB only the absolute necessary data will be disclosed in this report.

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2 Rolls in general

There are several parts in a roll that determines the characteristics of it. The most important parts in this project is the roller body and shafts. The roller body is the part of the roll that is in contact with the slab or another roll and the shafts are what connects the roll to the roller seats. The rolls connects to the seats with bearings that can handle misalignment’s, allowing the shafts to bend without damaging the bearings.

Illustration of a roll with the mentioned parts shown in Figure 5.

Figure 5: Illustration of rollerparts.

2.1 Work roll

The work roll used by SSAB is a cylindrical shaped roll with a hardened chromium alloy shell and a core of spheroidal cast iron as shown in Figure 6.

Figure 6: Cross section of the work roll.

The roll is made by made by Eisenwerk Sulzau-Werfen according to their VYS-standard with mechanical properties as described by Table 1 according to the ESW (2021) product data sheet.

Table 1: Mechanical properties relevant to ﬁnite element modelling for Eisenwerk VYS-standard work roll.

Part Young’s modulus [E] Poisson’s ratio [ν] Density [ρ]

Shell 215-225 GP a 0.30 7600 Kg/m³

Core 160-190 GP a 0.23 7200 Kg/m³

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2.2 Backup Roll

The backup roll is made by Union Electric Åkers and is cast steel roll, exact mechanical properties could not be found for this roll. Since the backup roll is not in contact with the hot slab and is continuously cooled and lubricated by a spray of cold water, standard mechanical properties for steel in room temperature was used as they should not deﬂect much from them. The mechanical properties used is shown in Figure 2 below.

Table 2: Mechanical properties relevant to ﬁnite element modelling.

Backup Roll 208 [GP a] 0.30 7760 [Kg/m³]

The backup roll has unlike the work roll a homogeneous cross section with a hardened surface. The contact surface of the backup roll is ground to a 2D-profile which consists of a flat part in the middle which passes on to an arc at a specific coordinate. The Arcs the passes on to a line by grinding in a chamfer towards the ends of the contact surface as described by Figure 7 below.

Figure 7: Illustration of backup roll proﬁle as described by grinding schematics.

As well as the 2D-Proﬁle or crown as it is also called, the backup roll also has conical shafts to give extra stiﬀness to the roll. It also has some minor edge blends and chamfers which are not needed for the simulation.

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3 Mechanisms of failure

There are many possible mechanisms of failure in the hot rolling mill system. The most common ones are due to fatigue, wear and wear that accelerates the fatique.

3.1 Fatigue and spallings

Callister (2006) deﬁnes fatigue as "a form of failure that occurs in structures subjected to dynamic and ﬂuctuating stresses"(p.227). The rolling mill is a very good example of such a structure as any roll in the mill experiences both stresses from dynamic bending and compression. Consider the load case shown in Figure 8 below, A roll subjected to bending torque and rotation.

Figure 8: Loadcase illustrating bending and rotation.

As the torque M in Figure 8 increases the roll bends upwards in the direction u. This causes tensile stress on the upper side of the roll and compression stress on the lower side. As the roll rotates the stress in the black point in Figure 8 cycles between tensile and compression stress as shown in Figure 9 below.

Figure 9: Stress cycling from dynamic bending.

As seen in Figure 9 the stress cycles between a positive and negative max value. The fatigue lifetime of a component is deﬁned by the amount of stress cycles and as is shown in Callister (2006) the size of the the stress min and max values has big eﬀect of the components fatigue lifetime. The dynamic bending is however not responsible for the spalls in a rolling mill instead it typically causes brittle failures in the transition between the rolling body and the shaft.

According to Schröder (2003) dynamic compression is the main culprit for the spallings as the contact forces and the stresses from it are much bigger then the bending stresses in the areas where the spalling’s mostly occur. The dynamic compression works in a similar way. Consider a rectangular element located in the domain of a slice in a backupp roll pressed down on a work roll as shown in Figure 10.

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Figure 10: Illustration of dynamic compression in a roll pair with a backup roll rotating with a velocity R, pressed down on a work roll with a force F .

As seen in Figure 10 the element is only at stress when it is in contact with the work roll. This is where the load distribution becomes so important. Almost every rolling mill has a load distribution as shown in Figure 11.

Figure 11: Load distribution between backup and work roll in a rolling mill.

The spallings most commonly occurs around the pressure points, this is why there is a strong incentive to reduce the force on the pressure points. Because reduced force in the pressure points means lower stresses in the roll which in turn gives a longer fatigue life. The load distribution is also highly dependant of the shape of the rolls.

And this is why the geometry of the backup roll can be adjusted to ﬂatten the load distribution as shown in Figure 12.

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Figure 12: Ideal load distribution vs a common load distribution.

3.2 Wear

Bhushan (2001) states that the mechanisms of wear can be divided into 4 categories of wear.

1. Abrasive 2. Adhesive 3. Fatique 4. Corrosive

All of these mechanisms occurs in the rolling mill system. Even grain corrosion could be triggered by tensile stresses and micro fractures which means that corrosion could be reduced by adjusting the load proﬁle. The adhesive, abrasive, and fatigue wear does however contribute more to the wear on the rolls. One of the most fundamental wear model is Archard’s law of wear, published in Archard and Hirst (1956). Where the the Worn volume W is expressed as a function of a wear constant K, The sliding distance s, contact force P , and the hardness of the softest material Pm. The worn oﬀ volume is expressed by

W = KsP . (1)

P_m

By studying Archard’s equation one can see that the wear is, proportional to the load and sliding distance between the bodies. This means that there have to be a diﬀerence in speed between the bodies to get a sliding distance. This is an important to understand where and why wear occurs in the rolling mill.

Between the work and backup roll there is a lot of force and high pressures but almost no slip between them.

Instead the dominating wear in the rolling mill is between the work rolls and the slab. As the slab is drawn in to the mill, its total volume cant change, instead the relationship between its height, width, and length must change. This is why the speed of the slab does not match the tangential speed of the work roll in the contact.

This is also the main reason why the work roll is the roll that is worn the most. Also note that the wear presented in the Figure 13 are diametrical and not radial.

Figure 13: Wear on work roll, picture courtesy of SSAB Borlänge.

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As the wear increases on the work roll, less energy is absorbed by the middle of the roll which means that more energy will have to be absorbed by the pressure points, thus increasing the peaks on the load distribution curve.

Figure 14: Increased peak load due to wear (red curve) vs load distribution with fresh rolls (blue).

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4 The ﬁnite element method

Logan (2016) Describes the finite element method a numerical method to solve differential equations that commonly occurs in engineering problems by dividing a geometry or domain into a set of sub domains or elements. For example it is a very efficient way to compute stresses and deformations on an object where no analytical solutions could be found. A finite element approximation can by discretisize it to a set of sub-domains or elements, nodes and boundary conditions and solving

[K]{u} = F (2)

For linear problems. Equation 2 is recognized by many as a way to compute the force required to compress or pull out a spring or a bar with stiﬀness K a distance u. By approximating geometries with diﬀerent types of elements with properties as for example a bar it possible to compute approximate displacements in linear deformation problems by solving a system of linear equations as shown in Figure 15.

Figure 15: Example of a ﬁnite element approximation of 1-D problem.

In the case pictured above a geometry without a varying crossection is approximated by three 1-dimensional bar elements with constant cross sections to compute the displacement u_iin the nodal points ni. Admittedly the discretization shown in Figure 15 is rough but as more elements are used the geometrical approximation gets better and better and the result converges to the analytical solution. For time dependant problems where the dynamic response is to be analyzed, equation 3 is used. Wang and Zhong (2017) describes it as the governing equation of structural dynamics.

M u¨ + Cu˙ + Ku = f (3)

M in equation 3 is the mass matrix, C is the damping coefficient matrix, and K the stiffness matrix. u is nodal displacement vector and u˙ and u¨ it’s first and second order derivatives which is velocity and acceleration. There are several types of elements which dictates the structures of the stiffness, damping, and mass matrix. They all have different properties and is used for different problems.

Equation 3 is solved in two ways in non linear ﬁnite element problems, either the by the implicit method or the explicit method. According to Dynamore (2021) the implicit method requires at least one or more inversion of the mass, damping, and stiﬀness matrix to solve the problem. The disadvantage with this is that matrix inversions is a computation wise heavy operation which means that it takes longer to solve equation 3 for each timestep. The advantage of the implicit method is that result convergence is guarantied thus making the implicit method suitable for simulations using longer timesteps. Explicit analysis solves equation 3 directly according to Dynamore (2021) which means that only one computation is needed for each timestep. This means that convergence is not guarantied and that the accuracy of the explicit solution relies on the timesteps being smaller than a critical timestep. This makes the explicit solver good for short simulations that requires high data resolution in a short time interval.

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4.1 Contact and penetration

To simulate interaction between parts, mathematical models which tracks and minimizes distances between diﬀerent sets of nodes and elements are needed. There are several methods for doing this, one of the most common one is the penalty method which is the one described in this chapter. According to Rust (2015) chapter 10 the gap g or distance between two bodies are determined by equation 4

g = ∆x − u. (4)

For a time transient simulation with a node to surface contact ∆x is the distance between a node and a segment for the last timestep and u the distance traveled between the last timestep and current one. When g < 0 the contact condition is full ﬁlled and penetration occurs as shown in Figure 16 shows.

Figure 16: Illustration of node to surface contact with nodal positon adjustment with the penalty method.

When penetration occurs forces must be added to the penetrating node to move it back to the surface so that the penetration is minimized. In commercial finite element software one of the most common ways is by using the penalty method or some variant of it. According to (Rust, 2015) chapter 10.2 the penalty method works by observing the potential energy of the system and adding penetration energy if the condition is violated to minimize the gap. As previously disclosed, this method is efficient but there is unfortunately trade offs in accuracy. It is quite common that some penetration exist even after penetration energy is added. Most finite element softwares allows the user to adjust penetration constants to customize the contact model in such a way that the penetration can be reduced enough to give accurate solutions. There are methods which eradicates the penetration completely but these are computation wise heavy and very inefficient to use time wise.

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5 Model simpliﬁcations

The rolling mill is a fairly symmetrical system, it is also big and needs many elements to get good result accuracy. Simulation wise this means that symmetry conditions can and should be used to reduce computation time. Quarter symmetry can be used to simulate the rolling mill if the following conditions are achieved.

1. The middle of the slab height wise does not deﬂect in up and down direction.

2. The oﬀ middle of the rolling mill does not deﬂect width wise.

3. The slab goes through the mill following a straight line.

Since these conditions are mostly true it was possible to construct the model as shown in Figure 17

Figure 17: Illustration of quarter symmetry model.

A strong reason for doing a quarter symmetry model was that it reduces the computational time without compromising the results. Since the roller seats are not an object of interest they were excluded from the simulations. The bearings were used as a system boundary since any material on the shafts outside of the bearings does not contribute to the bent shape of the rolls.

To create, compute, and visualize the load distribution, the programs listed below was used.

• Cad and pre-processing: Siemens NX 1899

• Boundary conditions, material properties, and solver: LS-PrePost 4.7 and LS-Dyna 9.7

• Data treatment and visualization: Matlab R2020b

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6 Cad and pre-processing in Siemens NX

The geometry of the rolling mill was deﬁned by a CAD-models, modelled in Siemens NX 1899. Siemens NX was also used to mesh and build the ﬁnite element models in the PrePost Application.

6.1 Backup roll model

The backup and work roll was modelled according to the drafts provided by SSAB Borlänge. To model the crown of the backup roll and be able to make changes to the geometry, the roller body was sketched and parametrisized according to the provided grind schematics as shown in Figure 18.

Figure 18: Parametrization of backup roll body, the shape is exaggerated for illustration purposes.

The proﬁle used for the initial simulation where the load distribution is computed has parameters as shown in Table 3.

Table 3: Backup roll proﬁle parameters.

Parameter a b c d f R

Value [mm] 0.8 257.5 42.5 1 745 775

These parameters builds the profile used by SSAB but in a slightly different way than how they actually grind it. By defining it this way, the radius between point f − b and b − c is self defined, meaning that improvements can be focused on parameters such as f and a without having to re-defining the radius for every attempt with new geometry. The sketch along with the measurements fore the shaft was then made into a solid with the Revolve function. At the end of the shaft, another body was extruded from it’s circular cross section. This body is there to simulate the boundary condition of a bearing in LS-Dyna. The backup roll is visualized in Figure 20.

6.2 Work roll model

The work roll was modelled according to SSAB’s drafts by ﬁrst generating a 2D-sketch and using the revolve function to ﬁrst create the core and then to create the shell. This was done to create two separate bodies which

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Figure 19: Approximation of wear proﬁle.

With NX’s analysis tool, measurements could then be taken and scaled according to the measurements presented in the raster image. The scaled measurements were then inserted into a new sketch in the work roll to create a curve which was the revolved and subtracted from the shell to produce the worn work roll 3D-Model.

6.3 The slab

SSAB Borlänge mill slabs varying in width between 700 to 1600 mm. However, the most common width is between 1530 and 1540 mm. In the data supplied by SSAB the un-deformed thickness of the slab was about 60 mm. For the computational model, the slab needed to be long enough so that the load distribution could be computed while the slab is in full contact with the work roll. The slab was modelled as a 30 mm thick, 400 mm long, and 770 mm wide cube to accomodate the symmetry conditions.

6.4 Assembly

To determine the components position in relation to each other they were added to an assembly as shown in Figure 20. The backup roll was inserted ﬁrst and the slab and work roll was then inserted and constrained to the backup rolls coordinate system. This made it possible to align work and backup roll and position them so that they are in contact when the simulation starts. The slab was positioned with a slight oﬀset in z direction so that the simulation does not start with penetration between the work roll and slab. Instead of applying forces in the simulation the bottom of the slab was positioned so that the thickness of the slab was 27 mm after it’s passed through the mill. The idea behind this is that instead of designing load curves that applies the right force at the right time, the rolls position is determined by a roll gap. The roll gap in this case is the gap between the upper and the lower work roll. This way force that acts upon the backup roll when the slab is drawn through the mill should be the same as the forces needed to applied to the rolls to give the slab the same deformation.

Figure 20: Work, backup roll, and slab in an assembly.

The yellow bodies in Figure 20 are rigid bodies used to simulate bearings and rotational drivers.

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7 Pre processing

The ﬁnite element mesh was created in Siemens NX Prepost application. The parts were meshed with a seed and sweep approach. To be able to do this kind of mesh, an idealized geometry were linked to the rolling mill assembly so that necessary changes could be made without changing the original geometry. The rolls were sectioned into quarters again and further sectioned to create sweepable bodies as shown in Figure 21 below.

Figure 21: Body sectioning for meshing.

7.1 Mesh design

It is very ineﬀective to use the same mesh size all over the mesh since this would mean that to get good enough resolution on the surface the amount of elements needed would be enormous. After some trial and error, the way to mesh the rolls was to use a "seed and sweep" approach which means that a 2D-Mesh is used to seed a 3D-Mesh which is generated by sweeping the 2D-Mesh along the diﬀerent bodies.

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Since the highest resolution was needed on the surface of the rolls and the mesh sizes were arranged so that ρ₁< ρ₂< ρ₃< ρ4. To create the 2D-Meshes that seeds the 3D-Meshes two 2D mesh collectors were deﬁned, one for each roll. With mesh sizes as described by table 4. Note that the 2D-meshes are not exported to LS-Dyna.

Table 4: Mesh sizes.

Mesh name ρ₁ ρ₂ ρ3 ρ4 Slab

Medium 20 mm 50 mm 100 mm 100 mm 10 mm

To create the 3D-Meshes to be sent to LS-Dyna six 3D mesh collectors and six physical property tables were created. The mesh collectors are whats holding the geometrical information like node id’s and their corresponding positions. The physical properties contains information such as part number, LS-Dyna material id, and element type. Each collector was given a name which describes which part it belongs to. The physical properties were given the same name as their corresponding mesh collector to keep track of what physical property belongs to which collector. To make sure that nodes of meshes belonging to diﬀerent bodies coincides a mesh mating condition was used. The 2D Mesh was then swept along the rolling body with element step size of 20 mm and then the roller shaft and the rigid body with element size 50 mm, forming 8-noded hexaedral elements over the rolls. When the quarter bodies were meshed, they were reﬂected two times to create half a roll. Meshing procedure shown in Figure 23.

Figure 23: Illustration of the mesh procedure for the backup roll. Yellow mesh indices the backup rolls rigid body

Since the reflection command was used, duplicate nodes were created. This means that there are two nodes in the same position and that the elements do not respond to the element next to it. An application in NX Prepost was used to find these nodes and merge them together. The same procedure done to mesh the backup roll was used on the work roll. The slab was meshed by sweeping 10x10x10 mm elements over it’s defining body. The complete mesh is shown in Figure 24, each colour indices a mesh collector destination.

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Figure 24: Complete mesh.

The element formulation chosen for all sections of elements were chosen to fully integrated 8-noded hexaedral elements. As the rolls contains elements where the heights is longer than the width the increased amount of integration points should help with the accuracy on the elements close to the middle. The same element formulation was chosen for the slab since it should be able to handle the plastication as long as the deformation of the element is not to extreme. The ﬁnal mesh is exported to a LS-Dynas format .k so that continuous modelling can be done in LS-PrePost.

8 Pre-processing in LS-Dyna

LS-PrePost version 4.7 was used to deﬁne boundary conditions, material properties, data outputs and solver settings.

8.1 Boundary and initial conditions

Since a quarter model is used boundary conditions for symmetry must be used. To deﬁne the symmetry conditions two node sets were created. The ﬁrst set contains all nodes touching the yz-plane (see Figure 24).

The nodeset was then fixed in the x-direction with the keyword BOUNDARY_SPC_SET. The same was done to the bottom of the slab except it was fixed in the y-direction. To simulate the shafts attachment to the seats the mid node of the rigid body attached to the backup roll was fixed in x,y, and z-direction with the keyword BOUNDARY_SPC_NODE, only allowing the rotational degrees of freedom. The node in the middle of the work rolls rigid body was fixed from movement in x and z-direction, allowing it to be pressed up against the backup roll.

To make sure that the slab is being drawn into the mill when the simulation starts a force of 1 kN was added on the back of the slab to push it into the mill. This was done with the keyword LOAD_NODE_POINT with the force being active for 0.05 seconds.

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8.2 Material models

The material model used for the backup roll,work roll’s core and shell body (dark blue mesh in Figure 24) was set to MAT_ELASTIC as no permanent deformation of the rolls was expected. The material parameters was set to the values speciﬁed in Table 5.

Table 5: Material data for elastic models.

Work Roll Shell 215 GP a 0.30 7600 kg/m³

Work Roll Core 160 GP a 0.23 7200 kg/m³

Backup Roll 208 GP a 0.30 7760 kg/m³

The material model used for the slab was the MAT_PIECEWISE_LINEAR_PLASTICITY model which is a simple but eﬀective model to use when permanent deformation and plastic material ﬂow occurs. This material model does not take thermal conditions into consideration so it is up to the user to input correct material properties in the form of a stress-strain curve. The piecewise linear plasticity model requires a yield function expressed by a set of points with coordinates [Strain,Stress] as shown in Figure 25.

Figure 25: True yield function for S355 at 1100^◦C and strain rate 10 s . −1

According to Dynamore (2017) The model uses the yield function to compare it deviatoric stresses at the current timestep to decide if it should treat the deformation as plastic or elastic. If the elastic conditions is not satisﬁed it computes the plastic strain for that timestep.

The data shown in Figure 25 was extracted from a complete thermal viscoplastic material model for S355 created by Swerim AB. Which made it possible to fetch data for the slab temperature and a speciﬁc strain rate. The viscoplastic thermal model was not used as it was computation wise much heavier than the piecewise linear plasticity model and needed additional thermal setups. Test simulations showed that the mean strain rate in the slab was about 10 s . Additional data needed for the piecewise linear plasticity model is shown in −1

Table 6 below. This data is needed for the model to compute relaxation and hardening, thus it is important to determine the nodes ﬁnal positions.

To deﬁne the rigid bodies MAT_RIGID was used. The density of the rigid bodies were set to 7700 kg/m³ Table 6: Additional data for S355.

Slab 7.00 GP a 0.30 7700 Kg/m³

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8.3 Contact models

To simulate the contact between diﬀerent parts, two models were tested. The ﬁrst one was LS-Dynas Automatic surface to surface contact which uses the penalty method to simulate contact. As the automatic surface to surface contact displayed some problems with penetration especially between the slab and workroll. The contact model was switched to AUTOMATIC_SURFACE_TO_SURFACE_MORTAR which according to Dynamore (2016) is a penalty based and robust contact model for implicit metal forming simulations, but also has support for explicit simulations. This model reduced the penetration issues a lot without having to do further analysis on penetration energies and compensation constants.

The model needed two contact interfaces. One for the interaction between the slab and the work roll, one for the interaction between backup and work roll. In both cases the work roll was assigned as the master part as it contained the hardest material. The friction coefficients used were 0.3 for static friction and 0.2 for dynamic friction in both contacts. These coefficients are rough estimates as in reality the friction coefficients depends on parameters such as temperature, surface roughness, lubrication, etc. The exact values for the friction is not important for the current simulation, what is important is that the backup roll does not spin against the work roll and that the work roll still manages to draw the slab through the mill without excessive slip.

8.4 Data outputs and solver settings

The solver was set up as for an explicit solution with default timesteps which means that LS-Dyna uses a timestep, computed by the systems critical timestep, this ensures that the explicit timesteps are small enough.

The critical timestep computed by LS-Dyna is about 4.5 microseconds and the timestep used ranges from 1.25 to 1.85 microseconds for the simulations in this project.

The plot steps was deﬁned by a curve shown in Figure 26. As seen in Figure 26 the solver takes plot steps of 0.01 seconds except for the interval where the t 0.1 < t < 0.15 where the plotstep is 0.0005 seconds.

Figure 26: Plot step curve.

To export the load distribution between the rolls a nodeset was defined along the backup rolls body with the create entity function. To reduce solution time the smaller plot steps were used when the nodeset passes the interface with the work roll and bigger plot steps when its not. To output coordinate and force data for the nodeset NODFOR and NODOUT options were activated in DATABASE_ASCII-OPTIONS keyword. The option to write a binary output file named binout was chosen for both cases and plot intervals were defined by the same curve which defines the timesteps. This generates force vs time and position vs time data for

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nodes x-coordinate is outputted from the simulation since the coordinates makes it possible to write a sorting algorithm based on each nodes coordinate. Since the coordinates should be arranged in rising order. To sort and plot the data a script in matlab was written. This script starts by data files generated by LS-Dyna and then extrudes the load and coordinate data for a chosen timestep which constructs a x-coordinate and a y-force vector. The script then creates two empty vectors xd and yd which are to be filled with values cordinate and load values in the correct order. To do this an algorithm was constructed with a while loop which relies on two predefined functions. The first one is the find function which according to MathWorks (2021a) outputs the index of the values it is fed with. To find the minimum values the min function was used which according to MathWorks (2021b) outputs the minimum value of an array or vector it is fed with. By combining find and min the index of the smallest value in the coordinate vector x could be stored in a varible d. When the smallest value in the coordinate vector is known it is used to insert the values of that index into the new vectors xd and yd. The same index is used to remove the smallest value from the start vectors before the while loop repeats it self. This way the algorithm dismantles the original vector and builds a new one with the right order.

In the transition between the radius and flat part of the rolling mill there is a shift in element size. This occurs because the meshing tool must fit elements around the shift between the flat line and the arc. This results in a bigger element on the radius side and a smaller element on the flat side. The effect of this is that less energy is required to deform a smaller element and more energy to deform a bigger element. This causes the node on the small element to display less force than the other elements and the bigger one more. This gives the load distribution irregularities in the form of two values which does not coincide with the rest of the distribution and a mean value between them. The best solution found for this problem was to remove these three values as shown in Figure 27. This solution may vary for some individual cases as this process has not been automated in the script.

Figure 27: Blue curve with irregularities and red with irregularities removed.

The last step in the post processing is to was to mirror the vectors around the the first elements so that the load distribution could be visualized over the whole backup roll. This is done as described by the following piece of code with the matlabs funcion fliplr which according to MathWorks (2021c) flips a vector left to right. The first three values of the vector were also removed in prior to flipping since the symmetry conditions interferes with how LS-Dyna plots the nodal forces. This means that when using quarter symmetry, the first two elements displays nodal forces that are to low before the solution converges. To solve this, the first three nodes were removed. Since this is not a problem when using half symmetry with whole rolls. a half symmetry model was used for comparison to make sure that this is a viable solution. Since the three values in the middle of the half symmetry model does not differ this method was deemed okay to use.

The full script is located in Appendix A.

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10 Load distribution improvement tests

Considering the load distribution from the simulations with standard rolls and its characteristics, it was decided that to improve the distribution more energy was needed to be absorbed in the middle of the roll.

To do this, a test were made where the parameter f which describes the length of the flat part of the work roll was reduced in 11 increments according to to see how the parameter influenced the load distribution. The last increment is an extreme case where f = 0 to test what happens if the flat part is removed completely and replaced with a radius. The tests were done with the lengths of the parameter f as shown in Table 7.

Table 7: Planned test for minimizing f

Increment 1 2 3 4 5 6 7 8 10 11

f [mm] 745 703.4 661.8 620.2 578.8 537.0 495.4 412.2 370.6 0

Based on the same idea of absorbing more energy on the middle of the roll a dual radius crown design was developed to be tested. On this roll, the ﬂat part of the roll is replaced with an arc.

Figure 28: Dual radius crown. Exaggerated for illustration purposes.

This design is based on SSAB borlänges current design whith the cad model following the same parametrication with the minor adjustments needed to create the dual radius crown.

11 Model validation

To make sure that the model responds as it should and gives accurate results there are several things to check for.

• The boundary conditions works as intended.

• The model behaves as it should and does not show nonphysical behaviours.

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11.1 Mesh size study

To make sure that the produced mesh gives accurate and feasible results a mesh study was made. The study was made by generating meshes with higher and lower mesh density and then compute the load profile to make sure that a finer mesh does not give a different result as this would mean that the mesh used is too rough.

Three 2D-meshes were designed with ﬁne, medium, and Rough mesh sizes. These were them swept across the work and backup roll to form 20 mm long elements.

Table 8: Table of mesh sizes for mesh size study.

Mesh name ρ₁ ρ₂ ρ3 ρ4 Slab Total number of elements

Fine 10 mm 40 mm 70 mm 70 mm 5 mm 609976

Medium 20 mm 50 mm 100 mm 100 mm 10 mm 169960

Rough 30 mm 60 mm 120mm 120 mm 20 mm 98920

After running the simulation the load distribution for the timestep with maximum values were plotted in the same plot for comparison, shown in Figure 29.

Figure 29: load distribution of maximum values for ﬁne,medium, and rough mesh.

As seen in Figure 29, the diﬀerence between the load distribution is quit similar for all cases. It in fact looks like it would be possible to use the rough mesh, especially since it only took 2.5 hours to compute the solution using 15 cores. The raw data from LS-Dyna shown in Figure 30 below paints another picture.

Figure 30: Nodal force data for rough medium and ﬁne mesh.

As seen in Figure 30 the data from the rough mesh is very noisy. There is also no way to identify when the node set experiences full contact with the work roll. The medium mesh shows a result almost as good as the fine mesh. Comparing the difference in solution time for the fine and medium mesh it was decided that the medium mesh which took about 5 hours to solve was the one that was the most efficient one to use since the fine mesh took over 20 hours to solve and the result of the medium mesh was deemed good enough.

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12 Results

The results of the simulation shows that the model works as intended. Figure 31 shows nodal displacement in x-direction which indicates that the rolls bends as they should according to the boundary conditions that acts upon them.

Figure 31: Nodal displacement in x-direction.

Observing the displacements of the backup roll, the displacements at the top of the rolls are positive and the lower parts are negative, indicating that the roll bends upwards. The displacements shown on the work roll shows that it bends forwards with the slab. Which is the correct behaviour for the work roll. This indicates that the boundary conditions work as it should.

Looking at the two contact interfaces shown in Figure 32 one can also see that the contact model works as intended as there are zero to minimal penetration in the system. The little penetration that can be noticed is so small that it should not inﬂuence the load distribution.

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12.1 Load distribution

The computational model and simulations yielded the following results. Seen in Figure 33 is the load distribution for SSAB Borlänges roughing mill when milling S355 steel 1540 mm wide.

Figure 33: Load distribution between new rolls.

Observing the load distribution in Figure 33’s it looks relatively flat as it should since SSAB has a very good idéa of what configurations work and what does not. By comparing the peak value and the value in the middle of the roll a good indication on how flat the distribution is. The max value in Figure 33 is 442.4 kN and the middle value is 341.5 kN . Which means that the difference is 90.1 kN or 23 %.

Plotting the load distribution from the simulation with the worn work roll with the fresh rolls as shown in Figure 34.

Figure 34: Load distribution between workroll and backup roll with new rolls and worn work roll.

Observing Figure 34, one can see that the peak load grows as the work roll wears. In fact it grows to 538.8 kN and the value in the middle of the roll is 341.5 kN which is a differance of 41%. As one might understand, this has very negative effects on the fatigue lifetime, which is a strong incentive to flatten the curves by adjusting the geometry of the backup roll.

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12.2 Improved load distribution

To ﬁnd a better load distribution the ﬂat part of the rolls were reduced by adjusting the parameter f . The most interesting results shown in Figure 35.

Figure 35: Load distributions from reduction of the ﬂat part of the roll.

As seen in Figure 35 The peaks load shrinks until f = 537.0 mm (purple curve), For f ’s smaller than that the peaks starts to increase again. If f shrinks any more the loads increases to much in the middle which will start to increase the peak again. For example notice the difference between load distribution curve for profile 10 and 6 (see Table 7) then finally continuous radius profile which is the extreme case of reduction of the parameter f . For the load distribution with the lowest peak found in this test, which is the one wheref = 537.0 mm. The maximum value is 410.1 kN and the middle value is 351.6 kN which gives a difference of 14%.

Two diﬀerent designs with a dual radius design was tested. The load distributions from these are displayed in Figure 36 with the load proﬁle for the original rolls for comparison.

Figure 36: Load proﬁles from tests with the dual radius design.

Figure 36 shows a significant improvement in load distribution flatness for both cases where the dual radius design is used. The best one (Dual Radius 2) shows a peak force of 404.5 kN and a middle value of 375.9 kN , giving a difference of just 7.1%.

Shown Figure 37 are load distributions from simulations of the dual radius and reduced ﬂat part designs compared to the load distribution from the original design.

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Figure 37: Comparison between diﬀerent designs of the backup roll vs worn work rolls.

As seen in Figure 37 both new backup roll designs shows reduction of the peak force in the load distributions.

In this case the best performing backup roll was the one with the flat part reduced to 537 mm. The peak force in the load distribution for this roll is 458.2 kN and the middle value 317.5 kN giving a difference of 31%. The dual radius shows a peak force value of 458.2 kN and a middle value of 317.5 kN giving a difference of 39%.

12.3 Conclusions

The simulations done considering new rolls in this project shows that the load distribution can be improved by adjusting the design parameters of the current backup roll proﬁle, and by using the dual radius design proposed in this project.

The simulations where a worn work roll is used shows that there is a lot to gain by using a shorter flat part of the backup roll. The reason that this roll shows an improvement in load distribution is that the backup rolls profile fits the worn work roll better, allowing higher energy absorption in the middle of the rolls. Therefore the best profile which currently can be recommended is the profile where f = 537 mm as it has proven the best compromise between low load peaks for both worn and fresh work roll.

It is possible to design a backup roll which ﬁts a work roll perfectly. This has been done but due to multiple shifts of element size the load distribution from that simulation had multiple irregularities on places were they could not be removed without compromising the validity of the result. It does however hint of a very good load distribution when the work roll is worn.

The dual radius design shows promising results in both cases. Considering that only two designs have been tested and already shows a signiﬁcant improvement for new rolls shows that further evaluation of this concept would be interesting. It should be possible to improve it further both for new and worn work rolls.

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12.4 Discussion

The method used to compute the load distribution between the rolls in SSAB’s roughing mill proved to be successfull as it gives accurate answers in a relatively short computation times. There are however things that can be done to improve the model further. By using a constant plot step for the graphics plot, computation times can be reduced to about two hours instead of ﬁve as the animation frames are heavy to produce, the last simulation done in this project was done this way. The plot frequency should be increased so that the data is written more times per second as some simulation missed the contact peak loads as the plot step does not sync with the explicit timestep. This led to some uncertainties regarding the scale of the load distributions for this simulations. The results showed in this report is however okay but this problem wasted some simulations that would have been interesting for the result.

Regarding the design parameters currently used for the design of the backup roll, tests for other parameters were planned for this project. There was not time planned for two weeks sickness which consumed the time planned for these tests. The goal with these tests was to ﬁnd the perfect combination of the parameters by varying them one at a time, using this model it should be possible to ﬁnd it.

The sharp eyed reader might wonder why simulations with worn backup roll has not been made. This is because the roll wear data came in picture form which meant that the wear had to be approximated by curves and lines and then scaled into the model. This was possible on the work roll as a good approximation could be found.

On the backup roll the wear had to be expressed in spline curves which were vary hard to scale into a model.

Considering how small the wear on the backup roll was, the assessment was made that simulations with only worn work roll was good enough. Had raw data from the measurements been provided more accurate results for the load distribution of worn rolls could have been produced.

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13 Future work

The simulations done in this project only consider one slab width and thickness for one pass. The same simulations could be done with the other widths and thicknesses that is milled to further get a better perception of what is going on inside the mill. SSAB also suggested simulations of a syncing process which is used to the calibrate the roller seats. In this syncing process the upper and lower work roll is in direct contact with each other. This could have strong inﬂuence of the fatigue lifetime as the stresses in the work rolls should be much higher than when milling steal due to the reduced contact area. This simulation was planned but discarded as it required to much modelling and modiﬁcation of the computational model to be able to complete it in time.

It is however highly recommended to do it.

To be able to do economical studies on how much money a better load distribution saves in reduced maintenance, a fatigue lifetime study should give valuable info on the rolls increased lifetime due to a better load distribution.

This could also help with planned exchanged rolls so that they don’t break in the mill. The model produced for this thesis could with minor changes be used for this as LS-Dyna oﬀers models to compute fatigue lifetimes.

LS-Dyna also oﬀers models to simulate wear, which means that the shape of worn rolls could be computed.

This could be used to compute the worn proﬁle and the load distribution of new designs of the backup roll before they are tested in the actual mill.

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C.R.F. Azevedo and J.Belotti Neto. Failure analysis of forged and induction hardened steel cold work rolls.

Engineering Failure Analysis, 11(6):951 – 966, 2004. ISSN 1350-6307. https://doi.org/10.1016/j.engfailanal .2003.11.005. URL http://www.sciencedirect.com/science/article/pii/S1350630704000238.

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William D Callister. Materials Science and Engineering: An Introduction. John Wiley and Sons, 2006. ISBN 0006970117.

Högskolan Dalarna. Hot Rolling Mill, Apr 2012. URL https://www.youtube.com/watch?v=AuuP8L-WppI.

[Online; accessed 26. May 2021].

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URL https://www.dynasupport.com/manuals. (2021-03-24).

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accessed 31. Februari 2021].

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stalmarknaden/varldsledande-stalforetag.

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14 Appendix A

%%LOADPROFILEPLOTTER clear all

% close all hold on

ts=44;

A=load("Y-Force.csv");

yp= A(ts,:);

B = load("X-Coordinate.csv");

xp = B(ts,:);

set(0,'DefaultLineLineWidth',1.5);

set(0,'DefaultLineMarkerSize',4);

set(0,'DefaultLineMarker','d')

while length(xp)>=1 %Sorting the values of xp and yp vector d = find(xp==min(xp));

xd = [xd xp(d)];

yd = [yd yp(d)];

xp = [xp(1:d-1) xp(d+1:end)];

yp = [yp(1:d-1) yp(d+1:end)];

end

%Removal of irregularities if 1 %1=on 0=off

yd(16)= [];

xd(16)=[];

yd(end-15)= [];

xd(end-15)=[];

yd(end-13)= [];

xd(end-13)=[];

end

%Removal of midpoints due to symetry error and vector mirroring.

xd=[-fliplr(xd(4:end)) xd(4:end)];

yd=[fliplr(yd(4:end)) yd(4:end)];

% PLOTS plot(xd,yd )

xlabel('Width [M]') ylabel('Force [N]')

Published with MATLAB® R2020b

Simulation of Rolling Mill to Computeand Improve Load Distribution