WO1996027454A1

WO1996027454A1 - Rolling mill vibration control

Info

Publication number: WO1996027454A1
Application number: PCT/GB1996/000507
Authority: WO
Inventors: Paul Roger Evans
Original assignee: Davy Mckee (Poole) Limited
Priority date: 1995-03-07
Filing date: 1996-03-06
Publication date: 1996-09-12
Also published as: GB9504510D0

Abstract

A rolling mill having an additional set of pass rolls engaging the strip on the inlet side, adjacent the roll stack, which are arranged to introduce a phase change into the mechanical system constituted by the tensioned strip and the mill stack structure, so as to inhibit unwanted vibrations of the mill.

Description

"Rolling Mill Vibration Control"

1. INTRODUCTION

1.1 PURPOSE OF ROLLING MILLS

This invention relates to rolling mills. The purpose of rolling mills is to reduce cast metal material to a saleable product. The material as cast is generally in the form of an ingot, perhaps half a metre thick, one metre wide and five metres long. The saleable product may be in the form of plates, perhaps one millimetre thick for making car bodies; strip, perhaps three hundred microns thick for making beverage cans; or foil, perhaps ten microns thick for wrapping chocolate bars. In each case the saleable product must meet specific requirements of dimensional accuracy, surface quality, metallurgical properties and cost.

1.2 TYPES OF ROLLING MILL

The route from as cast material to a saleable . product may involve in excess of thirty individual rolling operations, referred to as passes, on different types of rolling mill. Broadly speaking these rolling mills fall into two categories; single stand, where the material passes through a single set of rolls creating a single reduction in thickness per pass; or multi-stand, where the material passes through a number of sets of rolls creating a number of reductions in thickness per pass.

Some principles of rolling mill operation and dynamics will now be explained with reference to Figures 1 to 15 of the accompanying drawings in which:

Figure 1 shows the components of a rolling mill;

Figure 2 illustrates forces acting on the rolled material;

Figure 3 illustrates the mill stack mass/stiffness system; Figure 4 illustrates the mill stack natural frequencies;

Figures 5, 6, 7 and 8 illustrate the combined effect of forces and motion in the roll bite;

Figure 9 illustrates gauge tension interactions;

Figure 10 illustrates the relationship between exit gauge Ho and entry speed Vi;

Figure 11 illustrates the effect of strip entry tension T1;

Figure 12 illustrates the relationship between input and output waveform due to integral action;

Figure 13 illustrates the relationship between entry speed Vi and entry tension Ti;

Figure 14 illustrates the relationship between entry tension Ti and exit gauge Ho; and

Figure 15 illustrates the magnitude, phase and stability properties of the overall mechanical control loop.

1.3 COMPONENTS OF A ROLLING MILL

The layout of components of a single stand rolling mill is as shown on FIG.1. The material exits the entry coil; passes over the entry deflector roll; passes through the set of rolls where a reduction in thickness is made by the application of a rolling load; passes over the exit deflector roll; and finally enters the exit coil. The entry and exit deflector rolls being used to maintain the 'pass line¹ through the set of rolls with varying diameter entry and exit coils during the pass. The layout of

components of a multi-stand rolling mill is as for a single stand rolling mill but with additional sets of rolls between entry and exit deflector rolls.

A set of rolls, termed a roll stack, comprises of smaller diameter work rolls supported by larger diameter back-up rolls. Both the work rolls and back-up rolls are located by bearings within chocks. These chocks are in turn located within a pair of housings, one at each end of the roll stack. Mounted in the bottom (or top) of each housing is a large single-acting hydraulic cylinder, these are used to supply the rolling load and are termed the roll load cylinders. The combination of the roll stack, the chocks, the housings and the roll load cylinders is termed the mill stack.

The material is forced through the rolls by the application of a torque to the work rolls through the mill motor. Both entry and exit tensions are applied to the material by the application of torques to the entry and exit coils through the entry and exit coil motors, the former pulling against, and the latter pulling with, the direction of travel of the material. To summarize FIG.2 shows the forces acting on the material during a pass.

1.4 MILL STACK NATURAL FREQUENCIES

Within a mill stack the rolling load passes from the roll load cylinders, through the bottom back-up roll assembly, through the bottom work roll, through the

material, through the top work roll, through the top back-up roll assembly, and finally through the housings. Under the rolling load each one of these components will have some stiffness. In simple terms the housings will stretch, the rolls will bend, the roll contacts will flatten and the material will be squashed.

The mass of the mill components, being connected by their stiffnesses, introduces the concept of describing the mill stack as the mass-stiffness system shown on FIG.3. The calculation of the vertical natural frequencies

associated with this mass-stiffness system is well covered by published literature. For the first natural frequency, typically in the range 30 to 70 Hz all the rolls are moving up and down together. For the second natural frequency typically in the range 50 to 150 Hz, the top rolls are moving up and down in opposite directions to the bottom rolls. The previous two statements are summarised on FIG.4. 1.5 ROLLING MILL VIBRATIONS

A problem often experienced on single or multi-stand rolling mills are vibrations in the range 50 to 150 Hz. These vibrations occur above some mill speed threshold causing severe thickness variations of the material leaving the rolling mill and hence scrap material. This speed threshold cannot be predetermined causing mill operators to severely limit mill speed, and hence production, to ensure that vibrations do not occur.

Published literature show these vibrations to be 'associated' with the mill stack second natural frequency, indeed with reference to FIG.4, this explains the severe thickness variations as for this mill stack natural frequency the top rolls are moving up and down in opposite directions to the bottom rolls. In other word the rolls are 'bouncing' up and down on the stiffness of the material.

Although 'associated' with the mill stack second natural frequency these vibrations are not 'caused' by the mill stack second natural frequency, but the cause of the vibrations has not previously been recognised and hence no solution to the vibrations has been found.

2 THE ROLLING PROCESS

2.1 THE ROLL BITE

The material is deformed by the pressure applied by the work rolls as it passes through the space between them. The pressure applied by the work rolls is termed the rolling pressure with the space between them being termed the roll bite. The distribution of the rolling pressure within the roll bite is somewhat complex, however, it will suffice to state that there is a resultant vertical force that must be supplied by the rolling mill, with this

resultant vertical force being the rolling load as shown on FIG.5. 2.2 THE CONTINUITY EQUATION

A useful property of the rolling process is that changes in material width can be assumed negligible. With reference to FIG.6 this gives a simple relationship between material entry gauge Hi, entry speed Vi, exit gauge Ho and exit speed Vo in the form of the continuity equation:

H_iV_i=H_oV_o

Within the roll bite the material must, therefore, accelerate from Vi to Vo. If at any point within the roll bite the material gauge H_A-A could be measured the material speed V_A-A could be calculated by the extension of the continuity equation (Figure 6):

H_iV_i=H_A-A·V_A-A=H_oV_o

2.3 THE NEUTRAL POINT

At a specific point within the roll bite, referred to as the neutral point, the material speed must equal the peripheral speed of the work rolls Vr. On the entry side of the neutral point the material will be moving slower than the work rolls, on the exit side of the neutral point the material will be moving faster than the work rolls. As the material and the work rolls are forced together by the rolling pressure this action of the material and the work rolls slipping over each other creates high friction forces.

With reference to FIG.7 on the entry side of the neutral point these friction forces are trying push the material forwards, into the rolls, on the exit side the neutral point these friction forces are trying to push the material backwards, out of the rolls. To maintain

equilibrium the position of the neutral point is self regulating until the horizontal components of these friction forces balance.

F_B-F_F The effect of entry tension Ti and exit tension To on the neutral point is as shown on FIG.8. The application of entry tension Ti assists the friction force F_B to push the material backwards, hence, the neutral point must move forwards to maintain equilibrium. Similarly the application of exit tension To assists the friction force F_F to push the material forwards, hence, the neutral point must move backwards to maintain equilibrium.

F_B+T_i=F_F+T_o

The concept of the neutral point being self regulating dependent on the frictional forces in the bite and the applied tensions gives no clearly defined

relationship between entry speed Vi, roll peripheral speed Vr and exit speed Vo. For this reason and with reference to FIG.1 the mill motor is operated in speed control attempting to hold roll peripheral speed Vr constant, whereas, the two coil motors are operated in tension control attempting to hold entry tension Ti and exit tension To constant.

A change in entry tension creating a shift in the position of the neutral point has important implications on the process interactions discussed in Section 3. The shift in position of the neutral point creates a change in the distribution of the rolling pressure within the roll bite, in turn, creating a change in rolling load. In other words a mechanism exists within the roll bite the links horizontal and vertical forces, with a change in entry tension δT_i creating a change in exit gauge δH_o.

3 PROCESS INTERACTIONS

3.1 GAUGE TENSION INTERACTIONS

The cause of the rolling mill vibrations discussed in Section 1.5 are gauge tension interactions. For

reference the individual links within these interactions are as shown on FIG.9. The following discussion considers each of the individual links shown on FIG.9 with respect to changes around the mill operating point, as denoted by the S before each of the variables shown on FIG.9, for example, for a nominal entry speed Vi of 1000 metres per minute this discussion is concerned with changes in entry speed δVi of, say, 10 metres per minute.

For each of the individual links shown on FIG.9 plots of magnitude and phase, against frequency of the changes δ , are derived and explained. These individual plots are then combined to give the magnitude, phase and stability properties of the mechanical control loop

represented by gauge tension interactions. The exact scaling on all these plots is unimportant as the objective of the following discussion is only to give a conceptual understanding of the cause of the rolling mill vibrations discussed in Section 1.5.

3.2 EXIT GAUGE ┄> ENTRY SPEED

For the continuity equation (1) to remain valid a change in exit gauge δHo must be accompanied by a change in entry speed δVi or a change in exit speed δVo. To simplify this discussion a useful property of the rolling process is that, with reference to FIG.7, the neutral point tends to be close to the exit point of the material from the roll bite. Due to this closeness changes in exit gauge δHo can be assumed to produce considerably larger changes in entry speed δVi than changes in exit speed δVo.

Assuming constant nominal exit speed Vo, and for the purpose of this discussion constant nominal entry gauge Hi, a change in exit gauge δHo must be accompanied by a change in entry speed δVi and the continuity equation (1) becomes :

Hi(Vi + δVi) = (Ho + δH_o) V_o .... (3) More importantly, for equation (3) to remain valid a percentage change in exit gauge δHo must be accompanied by a percentage change in entry speed δVi, for example, a one percent change in exit gauge δHo at a nominal entry speed Vi of 100 metres per minute will create a one metre per minute change in entry speed δVi, whereas, a one percent change in exit gauge δHo at a nominal entry speed Vi of 1000 metres per minute will create a ten metres per minute change in entry speed δVi.

Returning to FIG.9 this simple percentage relationship enables the link between exit gauge δHo and entry speed δVi to be represented by a gain which increases with mill speed. This is as shown on FIG.10 with the magnitude plot being a horizontal line (constant gain at all frequencies) which moves up (increased gain) with mill speed. For clarification a gain has no associated phase lag, hence, the horizontal line on the phase plot at zero phase lag.

3.3 ENTRY SPEED ┄> ENTRY TENSION

A change in exit gauge δHo, creating a change in entry speed δVi, in turn creates a speed differential between the periphery of the entry coil and the speed of the material entering the roll bite. This is assuming that for the frequencies associated with the rolling mill vibrations discussed in Section 1.5 the peripheral speed of the entry coil is constant, the very large inertia of the entry coil ensures the validity of this assumption.

For changes around the mill operating point the length of material between the entry coil and the roll bite, passing over the entry deflector roll, can be considered as a pre-stressed spring, with the stress in this spring being entry tension as shown on FIG.11.

Assuming the entry coil end of this spring fixed, an increase in material speed entering the roll bite

increases the stress in this spring and hence increases entry tension, whereas, a decrease in the material speed entering the roll bite decreases the stress in this spring and hence decreases the entry tension.

Due to the effect of this pre-stressed spring it should be apparent that there is 'summing action' associated with the link between changes in entry speed δVi and changes in entry tension δTi. In other words, if a speed

differential between the periphery of the entry coil and material entering the roll bite was maintained with respect to time, eventually, the entry tension would either become so large that the material would break, or so low that material would go slack.

It is general to refer to this 'summing action' as an 'integral action' which, in turn, makes the link between changes in entry speed δVi and changes in entry tension δTi frequency dependent. To explain this dependency consider the example of 'integral action' shown on FIG.12. The waveforms on the left are at a frequency of 10 Hz, whereas, the waveforms on the right are at the higher frequency of 100 Hz, note the change in scale of the horizontal axis between the two sets of waveforms. For both sets of

waveforms the output waveform is the 'sum' or 'integral' of the area under the input waveform with respect to time.

The waveforms shown on FIG.12 can be used to explain the fundamentals of 'integral action' as follows :

3.3.1 Although the amplitude of the input waveforms are the same at both freqencies, the amplitude of the output waveform is an order of magnitude smaller at 100 Hz than at 10 Hz.

3.3.2 As the output waveform is the 'sum' or 'integral' of the area under the input waveform it lags behind by a quarter of a waveform or 90° phase lag. This 90° phase lag is consistent at both 10 Hz and 100 Hz.

Returning to FIG.9 this 'integral action' enables the link between entry speed δVi and entry tension δTi to be represented as shown on FIG.13. The magnitude plot slopes from left to right representing the decreased gain with increased frequency consistent with 3.3.1. The phase plot is a horizontal line at 90° phase lag consistent with 3.3.2.

3.4 ENTRY TENSION ┄> EXIT GAUGE

A change in exit gauge δHo, creating a change in entry speed δVi, creating a change in entry tension δTi, in turn creates a change in exit gauge δHo due to the shift in neutral point and hence rolling load discussed in Section 2.3.

Any change in rolling load has the ability to produce a 'forced vibration' of the mill stack mass-stiffness system shown on FIG.3, however, dependent on where it is created only some naturual frequencies of the mill stack mass-stiffness system are 'excitable'.

The changes in rolling load associated with gauge tension interactions, being created within the roll bite, have the ability to 'excite' the mill stack second natural frequency shown on FIG.4 as they can move the top rolls up and down in opposite directions to the bottom rolls. For clarification, they cannot 'excite' the mill stack first natural frequency as changes in rolling load created within the roll bite cannot move all the rolls up and down

together.

There is considerable published literature describing 'forced vibrations' of mass-stiffness systems. The relationship between a force acting on a mass-stiffness system and the resulting displacement is frequency

dependent. This dependency follows well established

patterns, at an 'excitable' natural frequency the

displacement becomes large and lags behind the exciting force by 90° phase lag, above an 'excitable' natural

frequency the displacement becomes small and lags behind the exciting force by 180° phase lag.

Returning to FIG.9 these well established patterns enables the link between entry tension δTi and exit gauge δHo to be represented as shown on FIG.14. The magnitude plot peaks at the mill stack second natural frequency, assumed for this discussion as 100 Hz, and then slopes away at higher frequencies. The phase plot passes through 90° phase lag at the mill stack second natural frequency and then slopes away to 180° phase lag at higher frequencies.

3.5 MECHANICAL CONTROL LOOP

The magnitude and phase plots for each of the individual links shown on FIG.9 can be combined to give the magnitude, phase and stability properties of the mechanical control loop represented by gauge tension interactions as shown on FIG.15. It is instability of this mechanical control loop at the mill stack second natural frequency that causes the rolling mill vibrations discussed in Section 1.5.

For clarification the scaling on the magnitude plots for each of the individual links is decibels (dB), defined by :

Being logarithmic this enables the magnitude plots to be combined by simply adding their values together. Similarly the phase plots can be combined by simply adding their values together to give the total phase lag for the mechanical control loop represented by gauge tension interactions.

There is considerable published literature on the stability properties of control loops, in particular, a control loop goes unstable if at 180° phase lag the magnitude plot is above 0 dB. With reference to FIG.15 the mechanical control loop represented by gauge tension interactions passes through 180° phase lag at the mill stack second natural frequency, with 90° phase lag coming form the link between entry speed δV_i and entry tension δT_i shown on FIG.13, and 90° phase lag coming from the link between entry tension δT_i and exit gauge δH_o shown on FIG.14. The increase in magnitude with increased mill speed, coming from the link between exit gauge δH_o and entry speed δV_i shown on FIG.10, completes the information on FIG .15.

For the lower rolling speed represented by the solid line on FIG.15 the mechanical control loop is stable as its magnitude at the mill stack second natural frequency is approximately - 6 dB, however, for the higher rolling speed represented by the dotted line on FIG.15 the mechanical control loop is unstable as its magnitude at the mill stack second natural frequency is just above 0 dB.

3.6 ADDITIONAL PASS LINE ROLLS

Accordingly, the present invention provides means for reducing vibrations within a rolling mill by adjusting the magnitude, phase and stability properties of the mechanical control loop represented by gauge tension interactions. Preferably, this is achieved by means engaging with the material close to the roll bite, for example, utilising one or more pass rolls. The

interposition of the additional roll(s) introduces phase advance into the mechanical control loop represented by gauge tension interactions in such a way that the frequency at which the phase lag passes through 180° is shifted well above the mill stack second natural frequency.

Some embodiments of the invention will now be described by way of example with reference to Figures 16 to 19 of the accompanying drawings in which:

Figure 16 illustrates possible arrangements of pass line rolls in accordance with the invention;

Figure 17 illustrates the resulting relationship between entry speed V_i and entry tension T₁;

Figure 18 illustrates the resulting magnitude, phase and stability properties of the overall mechanical control loop, and

Figure 19 is an axial cross-section through a pass roll.

The concept by which the additional roll(s) introduce phase advance is covered by the mathematical derivation given in Appendix A. Although Appendix A is written specifically for one roll the concept has been shown to be applicable to two or more rolls in accordance with options 2 and 3 of the possible arrangements shown on Fig. 16. This concept has been proven on a specifically designed test rig.

The criteria by which the additional roll(s) must be designed and installed can be summarised by: 3.6.1 The additional roll(s) must split the stiffness of the material between the entry deflector roll and the roll bite into two. To introduce phase advance the resulting stiffness of the material between the entry deflector roll and the additional roll(s) K₁ must be much smaller than the resulting stiffness of the material between the additional roll(s) and the roll bite K₂. It is for this reason that the additional roll(s) must engage with the material close to the roll bite.

3.6.2 The inertia of the additional roll(s) must be sized for the application in order to introduce phase advance into the mechanical control loop represented by gauge tension interactions over the required frequency range.

3.6.3 It is envisaged that in general two or more additional roll(s) will have be used in accordance with options 2 and 3 of the possible arrangements shown on FIG.16. These will be required to maintain a horizontal pass line of the material into the roll bite.

Returning to FIG.9 with the additional roll(s) the link between entry speed V_i and entry tension T_i changes from that shown on FIG.13 to that shown on FIG .17. Note the 'integral action' is still present, however, around the mill stack second natural frequency phase advance has been introduced.

This change in the link between entry speed V_i and entry tension T_i, in turn, changes the magnitude, phase, and stability properties of the mechanical control loop represented by gauge tension interactions from those shown on FIG.15 to those shown on FIG.18. Note on FIG.18 the phase plot passes through 180° well above the mill stack second natural frequency preventing the rolling mill vibrations discussed in Section 1.5.

For clarification, with the additional roll(s), there is the theoretical possibility of the mechanical control loop going unstable well above the mill stack second natural frequency where the phase lag passes through 180°. Returning to the hypothetical case shown on FIG.18, for the higher rolling speed represented by the dotted line the mechanical control loop is, however, still stable as its magnitude is approximately - 6 dB at the higher frequency. As - 6 dB represents a gain of two, this hypothetical case suggests the higher mill speed could be further doubled before this higher frequency instability occurs.

Referring to Fig. 19, a suitable form of pass roll construction comprises a solid fixed shaft 2 carrying a freely rotatable sleeve 4. The sleeve is made relatively low in mass so as to ensure that it does not "skid" on the strip but maintains good contact with it even at relatively high strip speeds. It is mounted on the shaft by means of bearings 6, 8 at each end which are kept lubricated by oilways 10 and 12 in the fixed shaft 2, with oil being pumped in at one end (10), passing behind bearing 6 and into annular chamber 14, along the surface of the shaft and exiting through annular chamber 16 and oilway 12.

Claims

1. A rolling mill comprising a mill stack with

additional strip engaging means adjacent the roll bite, said means being arranged to introduce a phase change into the mechanical system constituted by the tensioned strip and the mill stack structure, so as to modify vibration

characteristics of said mechanical system.

2. A rolling mill according to claim 1 in which the material engaging means comprises one or more additional pass rolls.

3. A rolling mill according to claim 1 or claim 2 further comprising an entry deflector roll upstream of the mill stack, said material engaging means being arranged between the entry deflector roll and the mill stack in such a position that the resulting stiffness of the material between the entry deflector roll and the engaging means is less than the stiffness of the material between the engaging means and the roll bite of the mill stack.

4. A rolling mill according to any preceding claim in which the said phase change is such as to shift the

frequency at which the phase lag of said mechanical system passes through 180°, to well above the second natural frequency of the mill stack.

5. A rolling mill according to any of claims 2 to 4 in which there are at least two pass rolls which are so

arranged that the pass line of the strip into the roll bite is kept horizontal.

6. A method of controlling vibrations in a rolling mill, comprising arranging a pass roll or rolls having suitable inertia in engagement with the strip on the inlet side of the mill stack in such a position as to introduce a phase change into the mechanical system constituted by the tensioned strip and the mill stack structure, so as to shift the frequency at which the phase lag of said mechanical system passes through 180°, to well above the second natural frequency of the mill stack.