ON THE DEVELOPMENT OF TOOLS FOR MECHANICAL DESIGN OF COLD ROLLING CLUSTER MILLS

E. Brusa^ L. Lemma^

^ Department of Electrical, Managerial and Mechanical Engineering, University of Udine, Italy ^ SKF Industrie S.p.A., Airasca (Torino), Italy

KEYWORDS: Cold Rolling Mill, Mechanical Design, Numerical Methods.

ABSTRACT. The paper investigates the main issues of design and modeling of so-called cluster mills for cold rolling of thin and moderate thin steel products, by means of numerical tools. This preliminary discus­sion summarizes the relevant aspects experimented on few operating cold rolling mills, started in [1], to select models and architecture suitable to build simple tools, to be used for a preliminary prediction of the dynamic response of the whole plant, in presence of known excitation, or even to simulate condition moni­toring operation, to support operators in signal processing of sensors equipping bearings and mill frame.

1 INTRODUCTION

The mechanical design of cold rolling mills usually involves several difficulties, due to the amount of phenomena governing the dynamic response of the w hole plant, mainly due to: interac­tion betw^een strip and working rolls, contact betw^een working and back rolls, bearings and supports, frame, damping effects and control systems, where present [1-8]. These aspects moti­vate the availability of a specialized literature mainly focused on rather simple models, with few rolls, and a large use of a direct regulation of the plant in operating condition, based on vibration monitoring and non destructive examination of the metal strip [5]. Available models demonstrate to be effective in case of 2-high and 4-high mill configurations and allow predicting, at least ap­proximately, the dynamic behavior of rolls and the related effects on the strip. In case of multiple rolls, i.e. cluster mill layout [9], including several supporting and back rolls, coupling effects make more difficult an effective prediction of the dynamic behavior as well as a fast regulation of the mill in operation, to avoid strip faults [4,6]. The latter affect the interpretation of the experi­mental results concerning the response in frequency domain of several parts of the mill, mainly back rolls, being usually the most monitored because of the accessibility for sensors application. The interaction among multiple rolls as well as the presence of several kinds of bearings and supports, even active suspension systems, joint to the role of localized damping and stiffness effects, made recently higher the industrial demand for process simulation and design tools to analyze the mechanical behavior, especially of cluster mills. It can be noticed that the aim of these tools is, more than an accurate analysis of the whole dynamics, the possibility to provide a quali­tative, simple and rather fast prediction of the trend of the process, under effect of known boundary conditions. Actually this need expressed by metallurgical engineering for numerical tools supporting process monitoring, was already experimented by automotive engineering in road test CAE services [10], where to tune vehicle parameters, for handling and comfort, particu­larly during the recent development of active control systems, the availability of simple models,

Published in: E. Kuljanic (Ed.) Advanced Manufacturing Systems and Technology, CISM Courses and Lectures No. 486, Springer Wien New York, 2005.

404 E. Brusa, L. Lemma

even running under Matlab environment, were welcomed. In the case of cluster mill a similar approach is followed: numerical models may be fast, possibly running in few minutes, based on few design parameters, to be tuned by experimental identification on the monitored plant [11-13]. The goal of this research activity is the selection of the numerical models suitable for predicting the relevant phenomena involved in cluster mill operation, to be tuned by direct monitoring of the plant, and to be used to simulate the effect of known excitation, faults or unforeseen actions on the dynamic response of the mill, and to allow operators performing condition monitoring to replicate numerically the generation of symptoms of failure detected on processed signals, to verify their origin, like it was performed by authors in [15].

2 SYSTEM ANALYSIS

To clarify the architecture of the numerical tool suitable for the above mentioned goal a descrip­tion of a paradigmatic cluster mill is herewith introduced as well as a list of phenomena to be predicted and avoided in operation.

2.1 CLUSTER MILL CONFIGURATION

A particular configuration of rolling mill is the so-called "cluster". Cold rolling occurs at room temperature, by cylindrical and smooth rolls, whose diameter is usually quite small to assure, in absence of benefits due to the temperature in hot rolling process, a suitable pressure on the rolled material. It is well known that rolling load is higher for smaller diameters of the roll, nevertheless slender rolls are prone to bend. Plant layout has to avoid this bending, by support­ing working rolls by secondary cylinders. Cluster mill is a typical solution: among several layouts proposed [5,8], Sendzimir mill or "20-high mill" is herewith investigated [Fig.l], to­gether with a more compact version, called "Z-mill" [1]. The number and the layout of rolls may change if another kind of cluster mill is considered, but the main strategy is common: working roll is supported by back rolls, which apply motion and all are supported by a crown of saddles or similar bearings.

Bands direction

Motion'-'':;;,,;. direction ^ ^ I

FIGURE 1. Sendzimir rolling mill sketch FIGURE 2. Examples of surface strip faults

Development of Tools for Mechanical Design of Cold Rolling Cluster Mills 405

Smaller rolls can roll high resistance metals and steel, to obtain very thin flat and to avoid intermediate thermal process. Layout in fig. 1 is suitable to provide the required stiffness to the working rolls (2) because of presence of a crown of additional rolls. The latter are supported by a first set of intermediate rolls (3), which are sustained by a second set (4), still consisting of intermediate rolls, and by the backing bearings (5), whose shafts (6) are supported by sad­dles (7). The transversal section of the plant looks like in figure 1 for the overall length of the rolls, but for working rolls (2), which have tapered conical ends, allowing a calibration of the plant, performed by moving them along the axial direction of the mill. Saddles (7) rotate in­stead of the inner rings of the bearings, fit on shafts (6). Rolls referred to as "PW" in figure 1, belonging set called (4), apply motion. Plant layout can be changed by acting on shafts called A, D, E, H, while shafts F and G tune the thickness of the steel flat. To assure the required flat quality, monitoring system measures the steel thickness, before and after cold rolling, and acts on the flat tension. Sometimes, additional hydraulic actuators are used to damp vibration on the intermediate rolls (3), in a closed-loop controlled based on the strip thickness monitoring. The mill may be reversible, if work rolls rotate both clockwise and counterclockwise, and steel strip is rolled in several steps, until the required thickness is achieved. Metal follows "front motion", when it moves from left-side to right-side and is subjected to a front tension, while it "moves back", and is loaded by a back tension, in the opposite direction.

2.2 STRIP FAULTS

Possible strip faults in rolling mill vibration include chattermarks, flatness faults and flat rupture [2-6]. Chattermarks appear often as periodical fault on the strip surface, thickness irregularity or waves [3]. Depending on the fi-equency interested by vibration problem three typical chatters are usually defined: torsional, appearing at lower values of frequency and depending on applied torque and motors control, so-called "gage or 3 ^ octave" and "roll or 5 ^ octave". Chatters of 3"^ and 5* octave are mainly due to technological and dynamic aspects. Material pre-damage, rotun­dity and balance errors upon rolls, roll bearings errors and drive irregularities cause usually speed dependent excitation, while a speed-independent evidence on waterfall diagrams acquired by monitoring system is due to self-excited or roll stand vibration, front tension fluctuation, material non-homogeneity, stick-slip, locking and drive control.

2.3 MODELING TASKS

Tools under development are required to include a suitable model of the whole cluster mill, to investigate the interactions occurring among the mechanical parts of the assembly, to predict the dynamic response of the plant and to simulate the monitoring operation of the sensors, whose location may be conveniently defined by running the numerical models to check observability and controllability of the rolls. To proceed straightforward a comprehensive analysis of the whole system to be modeled is sketched in figure 3. The goal of the numerical simulator is to provide a suitable prediction of either: the vibration perceived by the strip due to the motion of rolls, for a given excitation applied anywhere on the assembly, or the dynamic response detected and ac­quired by sensors, often located at the saddles of back rolls. In practice it consists of the solution of a set of equations of dynamic equilibrium of the assembled parts, with additional control ac­tions, if present. The main transfer function required by condition monitoring operators correlates

406 E. Brusa, L. Lemma

sensor signals and work roll-strip interaction, namely the force exerted on the work roll, which is usually measured by a load cell. Because of several phenomena occurring in the mill operation, additional excitation may be introduced by every roll composing the whole system. Moreover, if control systems are implemented models have to allow a closed control loop response for a given external action. In fig.3 several control systems may be identified: a rolling motion control, with strip speed feedback, a coiler rotation control with torque feedback, a motor torque control on powered rolls, while in perspective an automatic control may be implemented to correlate the response monitored on sensors (saddles) and motor or even coilers, or, in case of active control of roll vibration (not sketched), an hydraulic control of intermediate rolls, based on rolls position monitoring.

Saddles^ This part is

symmetric (see dashed axis)

Bearings

Dynamic contact between work and int. rolls

^rlp

Speed sensors, thickness measurement

Rolling motion control system

Interaction between work roll and strip

Role of the supporting

frame

Torque sensor

FIGURE 3. Exploded sketch of the Sendzimir layout modeled

Among the faults previously mentioned several may be investigated by the whole simulator. Since chattermarks depend on mass vibration, they may be studied, as well as effects of rotundity and balance errors upon rolls and drive irregularities. In case the model includes mill frame struc­ture, roll stand vibration is predictable. Very poorly predictable are front tension fluctuation, material non-homogeneity, stick-slip and locking. Figure 3 gives an overview of the main aspects to be modeled: vibration and control of rolls in contact; damping of bearings, supports and rolls; plastic behavior of the rolled strip, in contact with work roll, and lubrication; reactions of saddles and back bearings on back rolls; rolling motion and driving torque irregularities. All of these need for a numerical model. Actually two different levels of modeling may be foreseen. The whole system can be interpreted as sum of two subsystems, mutually interacting: the rolling motion with strip and coilers, and the mill with work and supporting rolls. Although in principle they are cou­pled by strip mechanical response, in practice a complete model, including all controls and parts

Development of Tools for Mechanical Design of Cold Rolling Cluster Mills 407

may be difficult to be run and tuned on the actual parameters of the mill. A preliminary assump­tion usually applied is that two subsystems are practically uncoupled, at least as first approximation. The latter is acceptable, when the object of the analysis is the dynamic response of mill to an irregularity of the strip action, being required to consider only the mill subsystem, or when a rotundity or balance problem on rolls is simulated, to detect the effect on surface irregu­larity of the strip and on the rolls vibration. The complete system is strictly required to be analyzed if a MIMO control is applied simultaneously to motor, rolling motion and rolls vibration and effects on strip are studied.

3 MODELING APPROACHES AND CLUSTER MILL PECULIARITIES

According to the previous discussion, which focused relevant issues of the analysis, to proceed further it has to be identified the influence of the whole aspects on the overall dynamic behavior of the mill and the numerical approaches to be implemented into the subroutines. This subject is herewith preliminary developed, by taking into account some experiments performed by authors on a Z-mill, described in [1] and on a Sendzimir mill (figure 4).

FIGURE 4. Sketch of the Z-mill and picture of Sendzimir mill used as test cases for experiments

3.1 MILL MODELING BY MULTI-D.O.F.: MULTI-BODY DYNAMICS, ROTOR

DYNAMICS AND PLANE LUMPED PARAMETERS MODELS

The available literature provides dynamic models based on the interaction between working roll and strip [5,6,14]. Usually 2-high and 4-high models include equivalent stiffness and inertia for supporting rolls and mill dynamics is numerically evaluated as vibration of work roll on the spring-damper equivalent system, representing the strip behavior. A first important result con­cerning cluster mill is that the role of all rolls is comparable, therefore model has to be based on multi-d.o.f system, where inertia of all rolls is considered, to find the critical points of the mill. Moreover, rolls more interested by vibration in chattering phenomenon are often supporting and back rolls in cluster layout, more than or at least as work roll, although this one applies to the strip the action determining surface faults and irregularities. The latter depends on the strip speed and on the frequency of the excitation and on mass and stiffness properties of rolls. Higher values of

408 E. Brusa, L. Lemma

Strip speed are more effective to induce vibration on rolls, by exciting resonances of the assembly. In the case of Z-mill [1] control rolls demonstrated to be the most excited by chatter at the corre­sponding frequency. As it is shown in figure 5, a wide range of frequencies is excited by chattering phenomenon, with severe amplitude on the control roll sketched in figure 4. It corre­sponds to the range between 3 kHz - 5 kHz. Amplitude of the dynamics response increases with rolling step, i.e. with strip speed on the mill.

liiiiii IBili

^ P i.Ai«

ik .^.^ ^^^/ SkHz/iiii

' —- / — f^^M

•i * */ -Ji^ / ^Ijjjlljl

1 ^JL*L ttJk "iut^^-^ 11. iri„iff/l tmUtmJt^i ^nm ». II

Fourth step

r l l l i l l i j l l

FIGURE 5. Waterfall diagram of Z-mill configura­tion, measured on intermediate/control rolls

FIGURE 6. Waterfall diagram of Sendzimir mill, measured on backup rolls

A second relevant aspect concems the use of plane, two-dimensional, models or three-dimensional ones. The question on the corresponding assumption is whether dynamic behaviour of rolls can be considered pure rigid motion or any flexural effect affects the dynamic response of the system, i.e. gyroscopic effect of rolls is relevant for simulation. Plane models, simply resulting from mass, spring and dampers assembly, according to sketch of figure 3, benefit of a lower number of d.o.f, assure fastness and are easy to be modified, by inputting new parameters during tests. They can be implemented in general purpose environment like SIMULINK and MATLAB. These are highly preferred in case of traditional mills, without cluster layout [8]. In case of big back rolls if results of a multibody dynamics code, like ADAMS, and MATLAB models are compared, vibration of rolls show a little influence of gyroscopy, because of the inertia and the layout of the mill, i.e. no conical whirling motion of rolls are apparently excited at the chatter frequency. This is the case of Z-mill [1]. Where inertial properties and stiffness of supports are comparable, like in Sendzimir configuration, the latter result is rather less evident. In particular modal analysis [16] and rotor dynamics [17] may be required to evaluate the presence of vibration modes and whirling motions respectively, dangerous for the frequency excited by the higher values of strip speed in rolling. In practice it can be observed that, because of the contact along the roll between two rolls and the high value of inertia of the whole rotors, usually no critical speed for flexural behaviour falls down the range of frequency explored by rolling operation, but whirling motion can be excited by unbalance, with amplitude sufficient to induce vibration on the adherent rolls, or even to modify friction between surfaces. In addition vibration modes often interest the extremities of the roll, shaped in a such a way that supports and bearings can be fitted. Example of this geometry is reported in figure 7. This effect suggests to discuss early the presence of vibration modes and critical speeds due to rolls, by performing a preliminary analysis of the

Development of Tools for Mechanical Design of Cold Rolling Cluster Mills 409

rotordynamic behaviour of the roll, by FEM as in figure 7. In this sense a three-dimensional model, including gyroscopic and inertial effects of the whole bodies is welcomed, while plane models look unsuitable to predict such aspect. Nevertheless is extremely difficult to include this dynamic effects in the whole mill model: multi-body dynamics codes, usually, do not run rotor-dynamic analysis subroutines, while compute the dynamic response of the rigid bodies suspended. On the other hand rotordynamics codes [17] basically assume the axis-symmetry of the analysed rotors, i.e. rotors composed by several rotating parts, having a unique rotation axis, and cluster mill configurations exhibit typically multiple rotation axes.

75.00 1 75.00 f-—75.00 + 75.00 4 — 7 5 . 0 0

FIGURE 7. FEM model of the end of an intermedi- FIGURE 8. Unbalanced magnetic pull effect on ate roll of Z-mill rotating shaft

3.2 ELECTROMECHANICAL ACTIONS

The above mentioned effect looks critical for powered rolls, where electric motors are connected. It is known that a significant whirl of the rotor induces an electromechanical instability by apply­ing so-called unbalanced magnetic pull, which causes severe damage on motor and rotating parts [15,18,19]. Figure 8 shows unbalanced magnetic pull effect: shaft rotating at angular velocity co, within the magnetic field rotating with spin speed cOm niay be subjected to a misalignment s, thus producing a whirling motion with angular velocity X, and a radial force towards the stator, rotat­ing with speed cOs . Because of the values very similar of speeds co, cOm, cOs, dynamic effect detected by motor sensors is often a beat response of rotor displacements, whose amplitude de­pend on the above mentioned spin speeds [18]. This phenomenon explains certain irregularities of rotating shafts in electrical machines, related to the grade of balancing applied to the rotor. It may affects mill waterfall not only at higher speed, but at lower speed too, with irregular peaks of excitation (figure 6). Unbalanced magnetic pull can be simulated in MATLAB subroutines [15].

3.3 MAIN NONLINEAR MODELS

The core of a numerical simulator includes a first model, describing the nonlinear interaction between strip and work roll (Bland and Ford; Johnson and Qi; Lin, Suh, Langari and Noah [14]). It computes stress and rolling pressure on strip and time evolution of vertical displacement of the work roll. The equation of motion of this submodel looks like:

410 E. Brusa, L. Lemma

m dt' + K{f)y = f = [ p(x)dx + J Cj-^T tan (f> dx (1)

where m is the equivalent mass of the whole subsystem, y the vertical displacement of the roll, K the equivalent stiffness, nonlinear function of forcing term / The main problem of the whole model is that friction coefficient C^ is poorly predictable by numerical methods, always needing for a model tuning on the monitored mill. Moreover while in case of 2-high and 4-high mills literature demonstrated that an average value may be introduced to analyze the dynamic response of the mill, in present case of cluster mill configuration it is numerically demonstrated that ex­perimental and numerical results match only when two friction coefficients in solving integral (1) for in-gauge and out-gauge respectively are introduced. Their values are strictly connected to lubrication condition at contact surfaces of supporting and backup rolls, which are affected by rolls vibration. Nevertheless the implemented model can be used to study the sensitivity of the whole mill to differential friction at in and out gauges.

^ 4J dx

a+5a h+dh

x1 x2

FIGURE 9. Model of roll bite according to [14] FIGURE 10. Example of ADAMS model of Z-mill rolls, with ends shaped to be supported by bearings

Two additional nonlinear models are introduced to predict the reaction of bearings in terms of elastic and damping forces (Harris [20]; SKF [21]) and the dynamic behavior of contact between rolls (Laursen [22]) into the overall mill model (figure 10). The first one is a typical relation be­tween force and displacement on bearing rings with nonlinear characteristic:

\-p

F F^~^

S k

dF_

dS F \-p

(2) kp pk^

being ^the displacement of ring material, F the applied load, k the stiffness of the whole bearing. Contact dynamics is modeled as impact force, combination of elastic and damping actions:

F-max{/r*(zo-z)^-c*z^(zo,j)} z<z^ -\<p<\ (3)

Development of Tools for Mechanical Design of Cold Rolling Cluster Mills 411

where supersigned ^* c* are stiffness and damping coefficients of the contact between rolls, ZQ is a reference position (usually the external diameter of roll), z displacement, \j/ is a rounded step function whose height is c(dz/dt) and width d (spanning the range ZQ - d to ZQ). Although the two latest models have been introduced in a preliminary implementation of the numerical tool, it can be noticed that coefficients are poorly predictable without a direct identification on the plant [11,12]. Moreover, while in 2-high and 4-high mills the latter stiffness and damping coefficients play a significant role in modeling effectiveness, in case of cluster mills supported by saddles numerical and experimental results show that the highest sensitivity of the model is towards stiff­ness and damping of saddles, more than bearings and contact among rolls. The most compliant part of the mill assembly, apart from strip, is located at backing rolls. ADAMS model of the test case Z-mill demonstrated that the latter is poorly sensitive to variation of contact (3) and bearing (2) stiffness and damping coefficients, if compared to a variation of values of the equivalent stiff­ness and damping of backing roll-saddles subsystem. This result is very important from the point of view of monitoring and control operations. About the controllability of the system: since often because of accessibility reasons saddles offer their external surface for sensors location, it can be realized that sensor is non collocated [23] with respect of the input force applied by strip on the work roll. It means that parasitic dynamics is present between sensor and strip due to the dynamic response of all flexible parts included, along the whole path. In fact this cannot be neglected, especially considering that the most active component is the nearest one, including backing rolls and saddles. Any control system operating on the signal processed by these sensors and regulating the force exerted by work roll may suffer significant effects of phase rotation. Moreover the ob­servability of the dynamic behavior of at least intermediate rolls may be significantly distorted by the localized effects occurring at saddles, where sensors operate. This results suggest to operate a preliminary observability and controllability analysis of the multi-body system, by means for instance of a plane model, to locate properly sensors. Currently encouraged solutions already proposed are sensored bearings [SKF,20] or even magnetic suspension technology with self-sensing capabilities [23].

4 CONCLUSIONS

This preliminary analysis was aimed to define some guidelines for performing numerical tools for the mechanical design of cluster mills for cold rolling. It was based on both a preliminary imple­mentation of models available in literature or even developed by authors. Relevant aspects of modelling as well as models have been tentatively listed and a selection among numerical ap­proaches, namely lumped parameters, multi-body dynamics, finite element method, was provided, by performing a screening of the influence of the whole phenomena on the overall mill behaviour. Some key features have been identified from condition monitoring and numerical investigations on test cases Z-mill and Sendzimir mill. The latter include lubrication and friction coefficient determination between rolls and on the strip surface, unbalanced magnetic pull effects at powered rolls, localized deformability of pins at rolls ends and delocalization of the most effective stiffness and damping at backing rolls, on saddles. These preliminary results are currently used to operate a suitable structuring of the numerical tool under development and to select suitable experimental configuration, mainly sensors position, for an effective model updating and identification of the relevant parameters to be tuned for supporting operating condition and monitoring activity.

412 E. Brusa, L. Lemma

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