The vibration of the leveling mill is common in metallurgical enterprises, which causes vibration marks on the surface of the support rolls and affects the surface quality of the strip. This paper establishes a bearing-rotor system model for a leveling mill, and finds that reducing the bearing clearance helps to improve the stability of the mill. The study of different speeds under the amplitude of the change, the work of the roll system gap changes on the vibration of the mill. Finally, the results of the study can provide reference for the theory of vibration suppression of rolling mills

Cai, Y. Q.

Dong, X. L.

Wang, J. W.

English

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257METALURGIJA 63 (2024) 2, 257-260X.L. DONG, J.W. WANG, Y.Q. CAISTUDY ON THE EFFECT OF WORK ROLL BEARING  FIT CLEARANCE AND SPEED ON THE VIBRATION  OF LEVELING MILLReceived – Primljeno: 2023-11-02Accepted – Prihvaćeno: 2023-12-28Original Scientific Paper – Izvorni znanstveni radThe vibration of the leveling mill is common in metallurgical enterprises, which causes vibration marks on the sur-face of the support rolls and affects the surface quality of the strip. This paper establishes a bearing-rotor system model for a leveling mill, and finds that reducing the bearing clearance helps to improve the stability of the mill. The study of different speeds under the amplitude of the change, the work of the roll system gap changes on the vibra-tion of the mill. Finally, the results of the study can provide reference for the theory of vibration suppression of roll-ing mills.Keywords: rolling mill, roll bearing, vibration, leveling, dynamies equationsISSN 0543-5846METABK 63(2) 257-260 (2024)UDC – UDK 621.771:621.822:66.084:531.717:531.3-517.9=111INTRODUCTIONLeveling mill vibration phenomenon is frequent [1] manifested as a new roll on the line after rolling a certain mileage support roll vibration mark phenomenon, forced to change the roll in advance, affecting the surface qual-ity of the strip [2], reduce mill productivity [3-4]. There-fore, many experts and scholars in the mill vibration monitoring and theoretical exploration and other aspects of in-depth research, from the leveling mill intrinsic fre-quency and trigger factors to carry out research, resulting in the leveling mill vibration and intrinsic frequency sim-ilar to or overlap caused by vibration amplification. In this paper, based on the consideration of vertical struc-tural support and bearing radial clearance, structural clearance change of work roll system and segmental non-linear problem [5], the vertical nonlinear vibration model under the influence of elastic rolling force is established to provide reference for the study of mill vibration and related vibration suppression theory.DYNAMIC MODELING OF AXIAL SEGMENTSConsidering the actual structure of the mill, a verti-cal vibration model of the structure shown in Figure 1 was developed. The shaft is discretized into 10 shaft segments, and the rolling force during the rolling pro-cess is applied to point 6. In addition, the rolling bear-ings are symmetrically distributed at node 3 and node 9, taking into account the nonlinear characteristics of the two bearings and the support when modeling the bear-ing dynamics. Each node is considered to have dis-X.L.Dong, J.W. Wang,Y.Q. Cai (E-mail: caiyq@ncst.edu.cn), College of Mechanical Engineering, North China University of Science and Tech-nology, Hebei, Tangshan, China.placement degrees of freedom in the x-direction and y-direction, and the system has a total of 22 degrees of freedom.Neglecting the influence of the corner, for the i th axial segmented unit, the node displacement can be ex-pressed in a fixed coordinate system as follows:  (1)The differential equation of motion of the elastic shaft segment is:  (2)In Equation 2,  is the unitary mass matrix of the shaft segment,  is the unitary inertia matrix of the shaft segment,  is the unitary stiffness matrix of the shaft segment, and  is the generalized force of the shaft segment.  (3)  (4)  (5)258  METALURGIJA 63 (2024) 2, 257-260X.L. DONG et al.: STUDY ON THE EFFECT OF WORK ROLL BEARING FIT CLEARANCE AND SPEED…Style:  (6)Bearing theory modelThe nonlinearities introduced into the rotor system by the radial clearance of the roller bearings are usually reduced to variable stiffness springs when analyzing the dynamic characteristics of the rotor system using finite elements.Rolling bearing force is obtained according to the Hertz contact force formula, the rolling bearing is de-composed into the inner ring, outer ring and ball, as-suming that the ball and the inner and outer ring for the pure rolling contact, as shown in Figure 2, and can be contacted and separated, the calculation is obtained to decompose the support force in the x and y directions as shown in the formula:  (7)where  is the contact stiffness coefficient and H is the H ( ) function - Heaviside function as follows:  (8)For bearings and bearing supports, the differential equations of motion are:  (9)SYSTEM DYNAMICS MODELBy assembling the matrix of each unit of the rotor shaft, the total finite element assembly matrix of the ro-tor shaft can be obtained. In the assembly process, the left node degree of freedom of the unit is connected to the right node degree of freedom of the neighboring unit on the left, and then the right node degree of freedom of the unit is connected to the left node degree of freedom of the neighboring unit on the right, and at the position where the left and right nodes are connected. ,  and are combined in the above manner, and after combi-nation, they are composed in the form of diagonal ar-rays.By using Eq. 2 and Eq. 9, the differential equation of the dynamics of the bearing-rotor system can be ob-tained as:  (10)Nonlinear vibration analysisThe radial clearance of the bearing causes localized shock phenomena in the bearing-rotor system, which is one of the important sources of nonlinear vibration in Figure 1 Physical modeling of the elastic shaft section of the work rollFigure 2 Bearing-rotor contact model259X.L. DONG et al.: STUDY ON THE EFFECT OF WORK ROLL BEARING FIT CLEARANCE AND SPEED…METALURGIJA 63 (2024) 2, 257-260the rotor system, and the radial clearance (0,05 mm, 0,1 mm) of the rolling bearing is investigated. The fourth-order Runge-Kutta method is used to solve the system numerically and obtain the time-domain response of the system. The time domain plots of the rotor system at node 6 are shown in Figures 3 to 6 for different rolling bearing radial clearances in the x and y directions, re-spectively.It can be seen from the above Figure: as the radial clearance of the bearing increases from 0,05mm to 0,1mm, the amplitude of the vibration signal also in-creases. When the clearance increases, there are obvious localized shocks and vibration fluctuations in the time domain waveform, which is due to the existence of radial clearance and thus reduces the support stiffness of the bearing, resulting in radial collision of the system.Figure 6 Y-direction time-domain map 0,1 mmFigure 3 X-direction time-domain plot 0,05 mmFigure 4 Y-direction time-domain plot 0,05 mmFigure 5 X-direction time-domain map 0,1 mmFigure 7  Relationship between fit clearance and vibration speed of 2 m/minAs can be seen in Figure 7, when the gap reaches 0,15mm, the vibration amplitude rises sharply. Through simulation, it can be seen that the larger the gap, the larger the vibration of the work roll, and the gap plays a role in amplifying the vibration.Figure 9  Phase diagram of the axial trajectory at a speed  of 7 m/minFigure 8  Phase diagram of the axial trajectory at a speed  of 2 m/min260  METALURGIJA 63 (2024) 2, 257-260X.L. DONG et al.: STUDY ON THE EFFECT OF WORK ROLL BEARING FIT CLEARANCE AND SPEED…In order to investigate the effect of input speed on the vibration of the system, five different input speeds (2 m/min, 7 m/min) are considered while keeping other factors constant. Figure 8 and Figure 9 show the varia-tion rule of the axial trajectory at different speeds, re-spectively.Increasing the working roll speed increases its cen-trifugal force. When the working roller speed is in-creased from 2 m/min to 7 m/min, it is obvious that the vibration amplitude of the system decreases.CONCLUSIONBy establishing a nonlinear vibration model of the bearing-rotor system, two conclusions can be drawn:(1) It is found that as the radial clearance of the bear-ing decreases, the vibration of the rolling mill system is smaller.(2) It is found that as the speed of the work roll sys-tem changes differently, the vibration system shows a stabilizing trend.Therefore, the appropriate reduction of the gap be-tween the work roll structure and the increase in speed will help to improve the stability of the system. The re-sults of the study can provide relevant theoretical refer-ences for the mill structure and vibration nonlinear problems.REFERENCES[1] Runlin C, Jiaxin L, Jie T, et al. Vibration characteristics analysis of rolling bearing rotor system considering radial clearance and outer raceway defect [J]. Advances in Me-chanical Engineering, 15 (2023)4.[2] Rongrong P . Nonlinear vibration characteristics and time-delayed displacement control of rolling mill under dyna-mic rolling force [J]. Journal of Vibroengineering, 23 (2021)7.[3] Rongrong P, Xingzhong Z, Peiming S. Vibration Characte-ristics of Hot Rolling Mill Rolls Based on Elastoplastic Hysteretic Deformation [J]. Metals,11(2021)6.[4] Hou D, Xu L, Shi P. Vertical–horizontal coupling non-linear vibration characteristics of rolling mill under mixed lubrication [J]. Journal of Iron and Steel Research Interna-tional, 28(2021)5.[5] Sun P Y, Zhang C D. Research on the Vibration of Rolling Mill [J]. Advanced Engineering Forum, (2011)2-3,1598.Note:  The responsible translator for English language  is Q.Q. Yin -NCST.

Study on the effect of work roll bearing fit clearance and speed on the vibration of leveling mill

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