Contact Load and Deformation Distribution for Sendzimir Rolling Mill Bearing System

Abstract: A contact and deformation analysis model is built for roll and bearing system of Sendzimir rolling mill，the solution is given by using finite element method. The contact load，contact stress and deformation distributions of Sendzimir rolling mill bearing system are analyzed and researched when the working roll is supported by one roll or two rolls under the given rolling conditions. The change rules are studied for contact behaviors of bearing system when supported by one roll under the different rolling conditions. The results show that compared to the case supported by two rolls, the bearing is subjected to higher internal contact stress and contact deformation when supported by one roll under the given rolling conditions. The internal stress and contact deformation of the bearing are significantly increased with the increase of rolling force when supported by one roll．

Key words: Sendzimir rolling mill; rolling mill bearing; roller bearing; contact load; contact stress; contact deformation; finite element

1. Preface

With the increasing demand for high-precision thin plate steel in the market, the twenty high Sendzimir mill has been rapidly developed and widely used, but its key technology research needs to be solved. The twenty high Sendzimir rolling mill has a sturdy frame cast as a whole, and the support roller device composed of bearings and mandrels is in the form of a multi support beam. The rolling force is distributed radially to each support roller device through the middle roller, and then transmitted to the overall frame along the length direction of the roller body. The support roller bearing rotates with an outer ring, with a linear speed of 800-1 000 m/min. The unit pressure it bears is 2-4 times higher than that of ordinary bearings, and the PV value is 3-20 times higher than that of general purpose-bearings. However, due to technological limitations, products are often prone to failure phenomena such as fatigue, fracture, and burning.

Sendzimir rolling mill bearings are high-tech products in metallurgical bearings. The research on the core technology of this product involves the identification and integration of many grouped key technologies. The development of Sendzimir rolling mill bearing technology is the most mature in Europe's SKF and Schaeffler, while Japan's KOYO, NSK, and the United States' Timken have also reached a high level. However, there is extremely limited technical literature related to this type of bearing that contains many advanced technologies. Reference conducted numerical simulation on the vibration characteristics of the Sendzimir rolling mill roll system, based on which failed rolling mill bearings were identified; Previous studies have simplified the support roller device to a solid roller, using a simple finite element model and contact element method to analyze the effects of rolling force and sheet steel strip width parameters on roll deflection and roll gap pressure distribution. However, this simplification is not applicable to the research of Sendzimir mill bearings and support roller bearing systems. The research on the contact force and deformation inside the bearing unit of the Sendzimir rolling mill and between it and the rollers is also extremely rare.

In terms of design structure, the roller backing bearing and the spindle together form a support roller system. The research not only involves the interaction relationship between the overall bearing unit and the intermediate roller, but also involves the interaction relationship within the bearing components. In addition, due to the fact that the four upper support rollers of the rolling mill and their corresponding intermediate rollers have single or double roll support forms, the internal mechanism of the bearing unit is also different. On the other hand, considering that each support roller has 5-8 sets of bearings to form a backing support roller bearing system, the research is more complex. Therefore, the systematic identification of key technologies and technology integration for Sendzimir rolling mill bearings can be carried out using the decomposition complex model method. For example, first, study the contact behavior of bearing units with single or double roller supports; Then, under given external conditions, conduct research on the contact mechanism inside the bearing unit; In addition, research on raceway design or roller macroscopic and microscopic topological structure design techniques around bearing microscale design can also be carried out, including so-called convexity and clearance analysis; The contact mechanism for controlling the H-value difference in the wall thickness of the outer ring of the bearing is also included in the group key technology research involved. Therefore, the research and development of Sendzimir rolling mill bearing products is a systematic and high-end bearing feature research work with group key technologies identified and integrated item by item.

As an important work in the identification and integration research of key technologies for bearing grouping in Sendzimir rolling mill, the following will focus on the coupling system composed of rollers and bearing units of a typical twenty high Sendzimir rolling mill with high speed, heavy load, and precision characteristics, and establish a mechanical model for studying the contact behavior mechanism of the interaction between bearing elements and roller systems; Through comparative research, analyze the contact behavior between bearing units with single and double roll support forms and intermediate rolls under different rolling force conditions; At the same time, research and analyze the contact behavior of rollers inside the bearing unit to support the distribution of contact stress and deformation between the bearing unit and the rollers; Through the above research, numerical experimental mechanism analysis basis is provided for the identification of micro scale design technology, process control technology, and installation and service technology of Sendzimir rolling mill bearing products.

2. Models and Methods

2.1 Roller bearing system model

The working principle of the twenty high Sendzimir rolling mill is shown in Figure 1. The rolling force Fz of the twenty high Sendzimir mill is transmitted from the working rolls S and T to the support roller devices A, B, C, D, E, F, G, H through the intermediate rolls I, J, K, L, M, N, O, P, Q, R; And ultimately transmitted to a sturdy overall frame to ensure a small thickness deviation of the steel strip in the width direction. The backing bearing of the Sendzimir rolling mill operates under high speed and heavy load conditions, with its outer ring serving as the working surface of the support roller in contact with the intermediate roller. Each support roller is usually equipped with 5-8 sets of two or three row cylindrical roller bearings as backing bearings installed on the same spindle. The rolling force is transmitted through the non-conformal contact between the outer ring and the intermediate roller, which is prone to deformation and changes the internal load distribution of the bearing, affecting the bearing capacity. The four second intermediate rolls I, K, L, and N on both sides of the centerline of the rolling mill are transmission rolls, which are driven by an electric motor through a universal joint shaft; The two work rolls are driven by four transmission rolls and their frictional forces with the first intermediate rolls O, P, Q, and R. Experiments and installation have shown that different forms of fracture often occur in the outer ring of bearings. Therefore, under the premise of considering the internal structure design of bearing units, conducting research on the mechanism of contact behavior between the outer ring and the intermediate roller interface has important practical significance for the identification and development of microscale design technology for bearing products.

Figure 1 Roller System of Twenty High Sendzimir Rolling Mill

The research was conducted on a typical Sendzimir rolling mill bearing, and its structural form and basic design parameters are shown in Figure 2a, respectively. Considering the different support forms of bearing units, two mechanical models were established to study the contact behavior mechanism between the backing bearing units and the intermediate roll interface of typical Sendzimir rolling mills, as shown in Figures 2b and 2c. It is worth mentioning that based on the iterative nature of numerical experiments in contact mechanics, the established contact mechanics model has taken into account the issues of stress concentration and sensitivity to numerical experiments between all contact interfaces, in order to improve the efficiency and accuracy of numerical experiments.

Figure 2 Simplified Model of Roller Bearing and Its Support System

2.2 Operating conditions

As the position of the working roller is different, the direction angle of the force acting on each roller constantly changes, and the force is also different. Selecting unfavorable working conditions for analysis, the maximum rolling force Fz designed for this model of Sendzimir rolling mill is about 10584 kN, ignoring the friction torque of the roll system, and setting the rolling force on the centerline of the upper and lower working rolls, as shown in Figure 1; The roller system is symmetrically arranged, with each roller having a standard diameter. The contact load on the support roller is 6700 kN, and there are 6 sets of backing bearings on each support roller to obtain the rolling force and contact load of a single bearing.

2. 3 Contact mechanics model

Establish a finite element model of contact mechanics for the coupled system composed of Sendzimir rolling mill rolls and bearing units, for the analysis of contact performance between single and double roll support bearings and rolls [10] (Figure 3). The material mechanical performance parameters are shown in Table 3. During the modeling process, the length of the roller is slightly greater than the width of the bearing, ignoring the rest. Without affecting the calculation results, the bearing structure is appropriately simplified, without considering the influence of lubricating oil holes in the inner ring and sealing grooves in the outer ring of the bearing. The cage effect is simulated using circumferential and axial constraints of the roller, and mesh refinement is carried out in the areas where contact occurs and areas where stress concentration may occur to ensure calculation accuracy and numerical iteration efficiency. The contact mode between interfaces can be established using surface interpolation technology to select surface to surface contact mode. The AI single roller support model of the rolling bearing system has 77 contact pairs, and the BIJ double roller support model has 78 contact pairs. The setting of contact pairs is mainly to facilitate the control of the relative positions of potential interface nodes in numerical iteration of contact mechanics, and there will be no excessive statement here. In addition, the contact numerical algorithm adopts the augmented Lagrangian method.

Figure 3 Contact Mechanics Model of Roller Bearing System

Table 3 Mechanical Property Parameters of Materials

3. Calculation results

Through finite element numerical calculation, the contact performance between the bearing and the rolling roller under single and double roller support under the same working conditions is compared, and the stress and deformation distribution of the bearing supported by the single roller under different rolling forces is further obtained. Set 2 load sub steps, automatic time step size; The running time is about 30 minutes, and the single and double roller support models undergo 7 and 5 balancing iterations respectively, achieving stable convergence, reading and processing data. By doubling the mesh size, the relative error of the two results was within 5%, eliminating the numerical sensitivity issues caused by grid density and stress concentration during the numerical iteration process.

The comparison of stress and deformation distribution of bearings supported by single and double rollers under maximum rolling force and given clearance of 0.1 mm is shown in Figures 4 to 6. Figures 4a and 4b show the distribution of contact stress between the intermediate roller and the outer diameter surface of the bearing unit along the width and circumference of the bearing under single and double roller support forms, respectively. Figures 5a and 5b respectively compare the deformation and comprehensive Mises equivalent stress distribution in the middle circumferential direction of the bearing outer diameter under single and double roller support. Figures 6a and 6c show the Mises equivalent stress distribution in the middle of the inner and outer raceway surfaces of the bearing when supported by a single roller, respectively; Figures 6b and 6d respectively show the Mises equivalent stress distribution on the middle surface of the inner and outer raceways of the bearing when supported by two rollers. When supported by single or double rollers, the contact stress distribution along the axis direction of the roller with the highest load is shown in Figure 7.

Given a clearance of 0.1 mm, the stress and deformation distribution of the single roller support bearing are shown in Figures 8 and 9 when the rolling forces are selected as 5000, 10000, and 15000 kN (i.e. the contact loads of the bearings are 527.5, 1055.1, and 1582.6 kN). Figures 8a and 8b show the distribution of contact stress between the intermediate roller and the outer ring of the bearing along the width and circumference of the bearing under different rolling forces. Figures 9a and 9b respectively compare the deformation and Mises equivalent stress distribution in the middle circumferential direction of the outer diameter of the bearing under different rolling forces.

The finite element solution and Hertz theoretical solution of the contact stress distribution of bearings under single and double roller support under maximum rolling force are shown in Table 4; The comparison results of the stress and deformation distribution of bearings supported by a single roller under different rolling forces are shown in Table 5, with the comparison values being the maximum values shown in the figure. It is worth mentioning that Hertz stress can only approximate the contact stress between simple characteristic contact interfaces. However, for precise analysis considering the overall structure of the Sendzimir rolling mill bearing unit and the contact behavior between the outer ring and the intermediate roll interface, its limitations are significant [11]. Therefore, the Hertz theoretical calculation results are only for reference.

4. Discussion

4.1 Analysis of contact performance of bearing system

From Table 2, it can be seen that under the maximum rolling force, the contact load of the single roll support backing bearing is the same as the combined force of the contact load under the double roll support, which is approximately 1116.7 kN. Under the same contact load conditions, compare and study the stress and deformation distribution of single and double roller support models with a given clearance of 0.1 mm.

From Figure 4, it can be seen that the contact stress distribution curve between the outer ring of the bearing and the intermediate roller is similar when supported by a single or double roller. Due to the fact that the contact load of the bearing is smaller when supported by double rollers than when supported by single rollers, the contact stress amplitude and contact width of the outer ring of the bearing supported by double rollers are smaller than when supported by single rollers. From Figure 6, it can be seen that the equivalent stress inside the bearing supported by a single roller is significantly higher than that of a double roller support. When supported by a double roller, 9 rollers are subjected to force simultaneously and relatively evenly, while when supported by a single roller, only 7 rollers are subjected to force, with significant differences in magnitude, which exacerbates the stress concentration phenomenon in the form of a single roller support. From the comparison between Figures 4 to 6 and Table 4, it can be seen that the stress and deformation distribution of bearings supported by a single roller is more concentrated and the values are larger than those supported by a double roller. Obviously, under the same working load and clearance parameters, bearings supported by a single roller are more likely to fail.

Figure 4 Contact stress distribution between the outer ring of the bearing and the intermediate roller during single and double roller support

Figure 5 Deformation of Bearing Outer Ring and Mises Equivalent Stress Distribution

Table 4 Comparison of Contact Performance Results of Bearing Systems

As shown in Figure 5a, when supported by a single roller, the outer ring of the bearing is φ = At 180 °, the deformation is relatively large, with relatively small deformation on both sides. The difference between the peak and trough of the wave is 0.171 mm φ = 90 ° and φ = The deformation near 270 ° is also relatively concentrated, with a drop of 0.065 mm, which can generate significant bending stress. Under the impact of the roller and the roller, it is prone to fracture and other failure phenomena; The deformation of the outer ring of the bearing supported by double rollers is relatively balanced, but φ = There is a certain sudden change at 142 °, 180 °, and 218 °, with a maximum drop of 0.102 mm, and there is also a risk of fracture. It can be seen that the non-conformal contact between the bearing and the roller can cause significant deformation and sudden changes in the bearing, changing its internal load distribution, and bringing adverse effects.

From Figure 5b, it can be seen that the Mises equivalent stress on the outer diameter of the outer ring in the contact area between the bearing and the roller increases significantly, which is caused by the overlapping contact between the outer ring, the roller, and the roller. The peak stress in other areas is mainly affected by the roller contact load. As shown in Figure 5b, the maximum stress value in Figure 6 is also generated by the simultaneous contact and superposition of the outer ring, the roller, and the roller. Other extreme points are mainly generated by the contact between the roller and the outer ring. From this, it can be seen that during the operation of the rolling mill, the contact performance parameters such as the peak stress of the outer ring of the bearing constantly change with the different relative positions of the rollers and rollers. The analysis in this article is only the most unfavorable fully superimposed working condition.

Figure 6 Mises equivalent stress distribution in the inner and outer raceways of bearings

From Figure 7, it can be seen that the maximum contact stress on the bearing roller when supported by a single roller is 2239.7 MPa, and the maximum contact deformation is 0.05 mm. The position is φ = At 180 °; The maximum contact stress and maximum contact deformation of the double roller support roller are 1363.3 MPa and 0.048 mm, respectively φ = At 142 °, 218 °.

Figure 7 Distribution of maximum bearing roller contact stress along the length direction of the bearing

4.2 Further Analysis of Contact Behavior of Single Roll Support Bearing System

According to the analysis results of the single and double roll support models, the contact state of the bearings is more dangerous when supported by a single roll. Therefore, given a clearance of 0.1 mm, the rolling forces of 5000, 10000, and 15000 kN were selected to further analyze and study the force and deformation of the bearings when supported by a single roller.

As shown in Figure 8a, when the rolling force reaches 5000 kN, the contact stress distribution is significantly shorter than the bearing width; When the rolling force is 10000 kN, the maximum contact stress is 1166.7 MPa, and the contact stress at the edge is close to zero. At this time, the size and regional distribution of the contact stress between the roller and the bearing are still relatively reasonable; When the rolling force increases to 15000 kN, the maximum contact stress reaches 1370.4 MPa, and there is a contact stress distribution throughout the width direction of the bearing. There is a stress higher than 160 MPa at the edge, which will increase the bearing capacity of the sealing areas on both sides of the bearing and make it prone to premature failure. From this, it can be seen that the structural parameters of the Sendzimir rolling mill bearings are compatible with the working load of the maximum rolling force of 10584 kN.

Figure 8 Contact stress distribution between the outer ring of the bearing and the intermediate roller under different rolling forces

Figure 9 Deformation and Mises Equivalent Stress of Bearing Outer Ring under Different Rolling Forces

From Figures 8 and 9, it can be seen that the contact width, contact stress, outer ring deformation, and Mises equivalent stress of the roller and bearing vary. As the rolling force increases, the phenomenon of deformation and stress concentration in the outer ring becomes more prominent: the maximum drop between the deformation peak and trough increases from 0.090 mm at 5000 kN to 0.164 mm at 10000 kN, and then to 0.223 mm at 15000 kN; The maximum drop between the stress peak and trough increased from 167.5 MPa to 295.0 MPa, and then to 404.5 MPa. From Table 5, it can be seen that the contact width, contact stress, and deformation of the outer ring between the roller and the bearing, as well as the Mises equivalent stress, all increase nonlinearly with the increase of rolling force. When the rolling force increases by two times, the maximum contact stress between the outer ring and the roller increases by nearly 86.8%, while the corresponding transverse and circumferential contact widths increase by about 14.3% and 41.7%, respectively; Meanwhile, the deformation of the outer ring and the Mises equivalent stress of the outer ring increased by 1.34 and 1.42 times, respectively. Taking into account the stress and deformation situation comprehensively, it can be concluded that overload conditions can easily lead to fatigue wear, fracture and other failure phenomena of bearings. In fact, the testing of the backing bearing of the Sendzimir rolling mill and the installation practice of the steel plant have shown that the fracture of the bearing outer ring and the adhesive wear caused by the lubrication failure between the outer ring and the intermediate roller interface are closely related to the working load, interface processing quality, and emulsified lubricant. The research results in the article can be used to provide a mechanistic explanation for similar problems. 

5 Conclusion

(1) The developed multi-interface contact mechanics model for the support roller bearing of Sendzimir rolling mill can obtain numerical simulation of the contact behavior mechanism of single and double roller support bearing systems under given rolling conditions.

(2) Under the same load conditions, the contact width between the outer ring and the intermediate roll in the single roll support bearing system and the Mises equivalent stress in the raceway are greater than those in the double roll support bearing system.

(3) As the rolling force increases, the contact performance of the single roll support bearing system changes significantly. This research result is conducive to further research on the contact behavior mechanism and failure mechanism of typical high-speed, heavy-duty, and precision Sendzimir rolling mill bearing units and roll coupling systems, providing a theoretical basis for the development of microscale design technology.

2023 November 4th week KYOCM Product Recommendation:

Linear motion rolling bearing:

Linear motion bearing or linear slide rail is a bearing designed to provide free motion in one direction. There are many different types of linear motion bearings. Mobile linear slideways such as mechanical slideways, XY worktables, roller worktables and some dovetail slideways are bearings moved by the drive mechanism. Not all linear guideways are motorized, and non-motorized dovetail slideways, ball bearing slideways and roller slideways provide low-friction linear motion for inertia or manually driven equipment. All linear guideways provide bearing-based linear motion, whether it is ball bearing, dovetail bearing, linear roller bearing, magnetic bearing or fluid bearing. XY table, linear platform, machine slide and other advanced slide rails use linear motion bearings to provide multi-axis motion along X and Y.