Coil Winding

August 21, 2017 | Author: Sourav Das | Category: Buckling, Rolling (Metalworking), Young's Modulus, Stress (Mechanics), Elasticity (Physics)
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Coil Winding...


The impact of coil winding induced problems in strip processing is described and the common causes of those problems identified. The criteria for designing a suitable coil winding strategy are listed and the constraints arising in typical strip processing plants discussed. Special attention is given to the development of head end tension practices, often referred to as “hardcore” tension policies, which minimise coil collapse and coil telescoping frequencies. A simulation model is employed to facilitate the strategy investigation. Suitably defined dimensionless parameters are introduced to reduce the dimensionality of the problem and to yield novel insights into the internal stress distributions of wound coils and the effect of mandrel shrinkage during winding. Finally, the effect of thickness profile and poor flatness upon the coil winding behaviour are described.

The Mystery of Coil Winding WJ Edwards Managing Director Industrial Automation Services G Boulton Research Engineer Industrial Automation Services

Copyright © 2001 Association of Iron and Steel Engineers


When the first hot rolled coils were produced off the ARMCO Butler hot tandem mill in the 1920’s it opened up a new era in metal strip production. Previously strip was processed in sheet form through hot and cold rolling, annealing, temper rolling, galvanizing and corrugating. Even so, the handling of strip material in coil form is not without its challenges as will be illustrated in discussions of the fundamental principles of coil winding technology. Coil winding and unwinding are the most frequent operations performed on flat strip material in its journey from the casting operation to the final manufacturing stage. So it is surprising that there is a negligible amount of information available which discusses the technology surrounding this operation compared with other companion processes such as rolling, annealing and coating. This situation would be understandable if there were no problems arising from coiling operations. However, the reality is that in many plants, particularly older ones, the costs of yield loss, speed restrictions, non-standard processing

and late deliveries attributable to poor coil winding are staggering with up to ten percent of production affected as it progresses through the plant. Whereas tens of millions of dollars are spent in upgrades of major processes to achieve modest yield gains, almost no resources are allocated to identifying, correcting and monitoring winding problems which are often responsible for a far greater loss of profit. Why this situation has arisen is difficult to explain except that winding appears to be deceptively straightforward and there are few measurements normally available with which to analyse the operation apart from the winding tension. Operator practices are often contributory causes to winding problems and management are reluctant to tackle such issues. Two other explanations for the lack of action are that the impact of the problem occurs one or more operations downstream and, over a period of time, an acceptance of damaged coils and their consequences can become part of the local culture. The information to be presented has been accumulated over a period of 25 years and will

hopefully provide a basis for future research on this important area. During this time a simulation model for calculating the internal stresses in a wound coil was developed and has been used to explore the characteristics of the process and to investigate optimum coil winding strategies. Subsequent sections of this paper will explain the application of this model to solving several common winding problems and provide a novel set of dimensionless parameters which simplify the task of designing an optimum winding strategy. The most frequent types of winding problems and their causes are also discussed.

a) Staggered Wrap Coil

Discussion of Coil Winding Principles

Anyone who has tried to wind a streamer of paper tape from a free ribbon of material into a tight wound coil will have discovered that it requires a reasonable degree of dexterity. Usually the sides of the coil are uneven and the coil does not behave as a solid cylinder unless the outer wrap is pulled tight enough to cause interwrap slipping which eventually results in a tightening of the coil wraps from the coil bore to the outer periphery. If the wraps are staggered when the coil is tight then it is difficult to push them back into alignment without damaging the wrap edges. The same issues discussed above in relation to a paper tape streamer also apply to metal strip coils. That is, coils should have straight sides and should behave as an integral, solid body while being handled for finishing operations. If inter-wrap slippage occurs during winding then scratching and surface damage often occur and there is a high probability of transverse movement of some wraps. The latter phenomenon is usually referred to as telescoping or dishing, depending upon the particular form of the resulting sidewall profile. Several examples are shown in Fig.1.

b) Dished Coil

c) Bore Stagger Coil Fig. 1 — Typical Examples of the Consequences of Interwrap Slippage

Table 1 Nominal Coil Winding Conditions Parameter








1 000



Youngs Modulus of base strip



Hardcore length (wall thickness)



Hardcore multiplier



Surface roughness



MPa -1


Surface initial approach distance



Mandrel diameter



Maximum pressure supported by mandrel surface



Mandrel friction coefficient on sliding surfaces



Mass of coil

Surface compressibility

An interesting plot of the lowest slip ratio within the coil and the corresponding critical wrap location during winding is presented in Fig. 2 for the nominal coiling conditions defined in Table 1.

Slip Ratio Slip Location



7 6



5 4 4 3 3 2



1 0

Critical Wrap Location (mm)


Minimum Slip Ratio (-)

In its more extreme form telescoping can present a significant danger to floor operators. The likelihood of this occurring increases as the coil diameter increases so that the trend towards bigger coils may lead to a growth in the incidence of coil winding problems. Interwrap slippage occurs if the torque applied to the coil by the tension on the outer wrap cannot be transmitted from wrap to wrap all the way to the coil bore. The torque transmission requires that the radial force between wraps, multiplied by the friction coefficient, is greater than the tension torque divided by the wrap radius. A term referred to as the “slip ratio” is defined as the ratio of the maximum tension torque which can be transmitted without slipping to the actual tension torque. The slip ratio must be greater than 1.0 for each wrap in a coil to avoid interwrap slipping.

0 0.1





Coil Wall Thickness During Rolling (mm)

Fig. 2 - Interwrap Slip Characteristics During Winding

The left hand axis is the lowest slip ratio and the location of the wrap most likely to slip is plotted against the right hand axis. Once the coil has reached the point where the high tension on the head end was removed the critical wrap becomes the one adjacent to the bore. Note however that since the slip ratio is well above unity there is little chance of interwrap slip occurring for this particular case. During acceleration and deceleration additional torques are imposed on the coil by the inertia forces. At the beginning of a coil, these are small, so their effect on interwrap slippage is small. During deceleration, the inertia forces are significant however they tend to counteract the tension torque so slippage is unlikely during deceleration. If rapid speed changes occur during winding, as may be introduced for thickness control corrections at the entry or exit of a tandem rolling mill, then these can lead to interwrap slippage and the loosening of wraps or telescoping in extreme cases. Coils wound with too low a tension may exhibit excessive deflections when handled, leading to scratching and, in an extreme situation, may collapse under their own weight so that a mandrel cannot be inserted in the eye of the coil. Coils affected by this so-called “soft collapse” condition will then need to be scrapped or recovered by extra processing. Coils may also collapse if the winding tension strategy is inappropriate. For example, if a tinplate coil is wound with a constant high tension then it may develop an elastic instability near the bore which will eventually propagate right through the coil wall. The end result of this form of “tight centre” collapse is a coil which can appear similar to a coil which has suffered collapse due to winding with too low a tension. (See Fig.3).


Soft collapse


Tight Centre Collapse

Fig. 3 - Examples of Collapsed Coils

Another issue which arises in coil winding is the interaction between consecutive processing operations. If a coil is wound on one unit with a certain tension strategy and unwound at the next operation with a markedly different tension then there is a significant risk that strip surface marking will occur. On the one hand, if the uncoiling tension is much lower than the original winding tension, then there will be a region of interwrap “creep” where the outer wrap leaves the coil and the tension undergoes a transition from the winding tension to the unwinding tension. The relative slip between the two outer wraps in the “creep” region can lead to surface scratching. Alternatively, if the unwinding tension is higher than the winding tension then interwrap slip can occur in the body of the coil with consequent scratching, dishing or telescoping as discussed previously. Unfortunately there are processing requirements on individual units

which may be incompatible with meeting the condition that the winding and unwinding tensions are matched. Examples of typical processing requirements are: • Cold mill entry: a high tension can be beneficial to rolling on the first stand. • Cold mill exit: a high tension aids flatness measurement and control and reduces the incidence of “soft coil” collapse. It also reduces the risk of skidding or rollgap instability in the adjacent rolling stand. • Annealing: low interwrap pressures are necessary to prevent sticking of adjacent wraps at the high temperatures occurring during the heating cycle. In general, low winding tensions produce low interwrap pressures. • Temper rolling: high uncoiling tensions are beneficial for optimising strip flatness and minimising sticker damage. They also reduce roll forces to acceptable levels on thinner products. For many products, primarily those which fall into the thick and wide category, the achievable tension levels are constrained by the capability of the coiling or uncoiling equipment. • Metal coating exit: The tensions need to be high enough to prevent interwrap slippage, which is more critical when the strip is oiled and the interwrap friction coefficient is low. The tensions must not be so high as to cause longitudinal wrinkling, an issue for thin strip and foil operations. On some units an ironing roll is necessary to avoid wrinkling and to keep air from being trapped between wraps. • Mandrel Characteristics: If the mandrel design is such that it limits the maximum stress on its components by allowing the mandrel diameter to shrink during winding, then care should be taken to ensure that the shrinkage is minimised by suitable tension strategy design. Mandrel shrinkage increases the likelihood of coil collapse and telescoping significantly by creating regions of low radial pressure and increased tangential stress compression. Once the regions of low radial pressure are created, they lurk in the coil ready to create dishing or telescoping problems later in the coil winding or during unwinding at the next process unit.

Strip Characteristics: The strip parameters which influence the winding behavior are thickness, width, hardness, Young’s modulus and surface texture. For a given material, the thickness and surface texture are the most significant because they effect the interwrap compressibility in the radial direction. Smoother strip is more prone to coil collapse and higher radial stresses, leading to an increased risk of sticking during batch annealing. (A study of collapsed coils some years ago revealed that the average surface roughness of collapsed coils was 67 percent lower than that of “normal” uncollapsed coils.) Clearly the winding tensions need to reside in a region which satisfies the constraints described above and are within the capability of the coiling equipment. Presentation Defects and Common Causes

A summary of common coil presentation defects and their most likely causes is provided in Table 2 (next page). The consequence of having non-flat coil faces is that the risk of handling damage from crane transport or placing the coils bore vertical is increased enormously with consequent non-standard processing costs and possible yield loss. The thinner the strip the greater is the risk of serious damage. Once a sidewall irregularity is created, it has the potential to aggravate processing at every downstream process stage until it is removed. For example, if a sinusoidal sidewall, or “sinwall” is caused by an instability in recoiling at a pickle line then the defect may be still observable after temper rolling. In the authors’ experience, many of the presentation problems stem from inadequate attention to mechanical maintenance and design. Common equipment items affected are mandrels, steering systems, process rolls and belt wrappers. The tight alignment specifications needed for good tracking of material are often not appreciated with unfortunate consequences. The outboard bearings on rolling mill mandrels are often misaligned or insufficiently rigid to perform their function satisfactorily. Coil collapse is normally controlled by tension strategy and head end thickness profiles. However, if mandrels become damaged or are not lubricated correctly then the incidence of collapse can increase. A particularly important

aspect of mandrel maintenance is the prevention of gaps or flat spots being created at the mandrel surface in contact with the strip as this allows the compressive tangential stresses at the coil bore to buckle adjacent wraps and subsequently propagate the collapse through the entire coil wall. A measure of the relative importance of the parameters which affect high tension collapse can be obtained from the elastic buckling criterion for a flat rectangular beam of length l and thickness h subjected to a compressive stress. The likelihood of buckling l2 may be shown to be proportional to where Eh 2 E s is the material Young’s modulus. The situation is a little more complicated when the strip has some curvature (See Chen and Wang [1]) however the dependence of the critical tangential buckling stress on the thickness squared explains why the risk of collapse increases rapidly below a certain thickness for a given mandrel size. Yuen has suggested expressing the collapse stability in terms of the unsupported length Lc needed to initiate buckling for a given compressive stress ó t and wrap thickness h . The approximate relationship proposed was: Lc = 0. 425 h



The units of Lc , h are mm and ó t is in MPa. The calculated length may then be compared with known imperfections on the mandrel. Measurement of Tension

When a tension force is applied to the winding of a coil, there is a component which is needed to bend the strip to conform to the shape of the coil outer wrap. Depending on the particular coil radius R, strip thickness h , width W and material yield stress ó y , there may be an elastic as well as a plastic bending component.

Table 2 - Coil Winding Defects and Their Causes DEFECT Staggered Wraps

Bore Stagger

Outer Stagger

Weld Stagger

Sin Walls

Bore Dip

Outer Dip

Hard Core Offset

DESCRIPTION Coil side position changes from wrap to wrap, giving coil wall and jagged appearance.

Ineffective centre guide control system

Coil centre wraps offset from rest of coil.

Alignment of mandrel and/or process roll; belt wrapper wear or alignment problem; level problems on head and tail end at rolling mill stand.

Outer wraps of coil offset from rest of coil

Alignment of mandrel and or process unit; mill level problems on tail end of coil rolling (possibly due to liner clearances)

Staggered wrap in middle of coil at location corresponding to weld

"Hook" or camber in hot rolling; asymmetry in thickness profile or hardness arising from hot mill; mill level problems if mill slows down to roll the weld.

Sinusoidal pattern on the walls of coil

Steering stability problem during recoiling, usually at pickle line for steel coils. Problem tends to be worse for thick wide strip. Cause may be instrumentation, passline geometry, control system design or roll alignment.

A dip in the coil wall shortly after the start of coiling.

Belt wrapper induced due to misalignment or wear. Can also be linked to acceleration effects in adjacent rolling mill stand.

A dip near the outer circumference

Mill deceleration level change due to mechanical effect in bearings or liners of process.

The coil core, rolled with a higher tension, is offset from the rest of the coil

Change in coiler alignment as tension changes from hardcore value to body value. Possibly outboard bearing related or mill stand chocks moving as tension changes.

Coil vertical cross section has a barrel shape

Can arise from the incoming coil or as a consequence of inter-wrap slippage (ie telescoping). Tension strategy and mandrel characteristics are critical. Larger diameter coils are more vulnerable to slippage towards the end of winding if the body tension is not gradually reduced to maintain a constant torque. If elastic sleeves in use, excessive tension may cause sleeves to be extruded as mandrel shrinks. Body tension too low. Dropped coil. Excessive coil lubrication.

Coil Barrel Dishing

Low Tension Coil Collapse

High Tension Coil Collapse


Non-circular, oval shaped, bore Non-circular, kinked bore which may eventually become oval if collapse propagates to outer wraps of coil.

Winding tension strategy, excessive mandrel collapse, poor flatness, (especially if manifest),smoother strip, excess carry over, mandrel imperfections, strip thickness profile, roll alignment, strip too thin on head end. Mandrel hydraulic pressure may need to be varied as coil is rolled. If coil is dropped, buckle may occur at lowest point in bore.

The elastic component is recovered when the coil is unwound however this is not true of the plastic component which is reflected in a change in strip thickness, width and length. This means that the effective tension in the strip in the coiled state is less than the externally applied tension. The measurement of winding tension force on many processes is achieved by an indirect inference from the mandrel motor parameters rather than from a direct tensiometer measurement. Often this involves measuring the motor armature current I A and relying on the motor calibration. This requires that the motor field is adjusted such that the motor emf is proportional to strip speed V . In this case the tension force of the coiled strip is given by the equations provided by Goodridge [2]:

Finally, it is important to note that even if a direct tension measurement is available, there could be additional bending losses if the strip passes over a deflector roll between the tensiometer and the coiler such that plastic bending occurs. Coil Winding Simulation Model Overview

The objective of a coil winding algorithm is to predict the axisymmetric radial and tangential stress distributions at all interior points of a coil in each stage of winding. At any particular instance during the coil winding process, these distributions are only a function of coil radius (see Fig. 4).

Coil Radius R

σt r

T f = kt I A − T fI − T fb  h2 R 2  T fb = σ yW  −   L1 3E s  J  V 2h  T fI = R2 V& − , R  2 πR 2  where k t is the conversion factor from current to tension force including the effect of losses, T fb is the tension force component required to bend the strip to the coil radius (elastic+plastic), T fI is the inertia force term due to line speed acceleration V& and reel deceleration due to the changing coil radius and J R is the polar moment of inertia of coil, mandrel and drive system. This approach can often lead to substantial errors, particularly on old equipment whose calibration has drifted. A more reliable method is to measure the motor armature voltage V A as well as the armature current I A and to use the following equation: VA I A − T fb − T fI V where η is the electrical energy conversion efficiency from the drive motor to the mandrel shaft. Tf = η

R0 Mandrel Radius Wall Thickness Lw

σr r r

Fig. 4 - Stress Distribution in a Wound Coil

Initial development of coil winding models took place in Europe in the 1950’s and a paper was published by Sims and Place [3], which derived formulae based on the theory of wire-winding of gun barrels. This theory, which was based on Lame’s stress equations for a hollow cylinder subjected to an external pressure, related the tangential and radial stresses on the mandrel to the strip coiling tension and the number of wraps. Their model was confirmed for the case of a small number of wound wraps. This work was subsequently extended in a thesis by Wilkening [4], who demonstrated that the theory of Sims and Place breaks down for more than 55 wraps, overpredicting the stresses by more than 200 percent after 100 or so wraps. Wilkening used an empirical correction to correct the model and obtained a better agreement with experimental results but he was unable to explain the non-linear dependence on the winding tension. An extension of Wilkenings’ analysis was provided by Altmann [5] who



m m)

Initial Approach = 1.4 (Smooth Strip) Initial Approach = 2.8 (Rough Strip)


Surface Seperation (

derived an analytical solution for the case of a constant radial elastic modulus. A radical change in the so-called “shrink-ring” model of Sims and Place was proposed by Wadsley [6], in which the interwrap compressibility in the radial direction was increased by a factor of 50 to 100 compared to the nominal value for the base material. The justification for this change arises from the interaction of surfaces in which the surface roughness is appreciable in relation to the nominal strip thickness. By incorporating the non-linear surface compressibility characteristics of the material into the shrink-ring model, all of the trends observed in earlier experiments could be reproduced. The assumed compressibility characteristic was one for which the change in the gap l between adjacent wraps obeyed the law: dl = −λ (σ r )dσ r , l where λ (σ r ) is the compressibility of the rough surface interface between wraps. The compressibility for steel and aluminium materials is independent of the contact stress for the range of stresses normally found in practice. In this special case the previous equation can be integrated to give the normal approach of the surfaces under load as: l = l o e (− λσ ) where λ is the average compressibility of a pair of strip surfaces and lo is the initial unloaded separation, approximately 3.0 to 5.0 times the cla roughness of the strip surface. Further discussion of this topic and the effect of superimposed oil films is provided by Wadsley[6]. Typical compressibility curves for two steel materials having different surface roughnesses are shown in Fig. 5. Whereas an uncoated steel surface may have a compressibility of 0.03 MPa-1 for tinplate and 0.075 MPa −1 for sheet product, galvanised material is much higher and typically in the range 0.25 to 0.75 MPa −1 . Comment on the measurement of these properties is provided by Yuen [7].






0 0











Normal Pressure (MPa)

Fig. 5 - Typical Compressibility Characteristics for Uncoated Steel Surfaces

Although there has been substantial progress made in the development of simulation tools to investigate coil winding phenomena, these tools do not appear to have been widely used to improve winding practices on mills rolling strip material. The potential benefits are not only in reducing coil collapse but also to avoid the unnecessary use of sleeves and to produce solid coils destined for batch annealing with lower mean tensions (to reduce interwrap sticking). The other important issue in simulating the winding of coils is to represent the deformation characteristic of the mandrel and any internal pressure relief mechanisms it may have. An analysis of this problem was published by Turley [8], and forms the basis for the simulated mandrel model. If the hydraulic pressure is insufficient to oppose the forces generated in the mandrel shaft by the wound coil, then the mandrel may partially collapse with a consequent increase in the risk of wrap staggering, coil dishing and bore collapse. In the authors’ experience, the majority of mandrels experience significant mandrel diameter contraction due to a combination of component elastic deflection and internal pressure relief mechanisms such as the hydraulic one just described. The model requires details of the strip surface compressibility. These are difficult to calculate on a theoretical basis due to the unknown effect of any lubricant films attached to the surface. Therefore this characteristic is best measured by compression testing a stack of discs punched from a sample of the rolled material. The coil winding analysis program has been formulated for cold rolling and finishing operations involving coated and uncoated materials. It is not suited to hot rolling or the

winding of very thick strip which may have appreciable bending stiffness. The model also assumes that no open gaps are formed between the wraps at any point. If a gap does occur, the analysis for that transverse section may be incorrect, however the analysis for the other sections will still be meaningful although some minor errors may arise. Each slice of the coil is assumed to have no interaction with those on either side of it, other than via the transverse strip tension analysis which only affects the winding tension of the outermost wraps. The input data to the program includes: • Mill coiler dimensions and collapse mechanism characteristics. • Non-linear wrap compressibility characteristics. • Product dimensions and elastic properties. • Coil winding conditions for strip centreline thickness, tension force or stress and temperature. • Material yield stress. • Interwrap friction coefficient.

stress which can become compressive if sufficient wraps are added. The radial gradient in the tangential stress at the coil bore is low at the time coil winding is complete. • When the mandrel is collapsed, bore wraps are released and some slippage occurs as they unwind. This is accompanied by a drop in the radial stress to zero at the bore and a corresponding increase (compressive) in the tangential stress. • After the coil is removed from the mandrel of a cold rolling operation it slowly cools to a uniform temperature leading to further growth in compressive tangential stress at the coil bore. The radial stress also increases however this effect is highest further into the coil. In general, the innermost wraps of a coil are in a state of highest tangential compression and experience the greatest radial pressure gradient. The following relation holds for any radius r :

Results are produced for each of the different states of the coil winding process, specifically:

 r   σ t = −1 + ∆σ r + σ r   h   is the pressure gradient across

• • • •

The “as wound” state prior to releasing the winding tension. After releasing the winding tension with the coil still on the mandrel. After removal from the mandrel. After cooling.

The results include the radial and tangential stress distributions throughout the coil as it is wound and the wrap slipping parameters. The characteristic pattern of stress buildup in the winding of a coil is as follows:

• • • .

When a wrap is added to the coil it is in tension and the radial stress at the outer wrap is quite low. As more and more wraps are wound the radial stress at the coil bore increases. The growth in the radial stress at the coil bore is accompanied by a corresponding decrease in the corresponding tangential

where ∆σ r wraps. From the above relationship it may be inferred that if the mandrel collapses in a controlled manner during coil winding, then the tangential stress will become more compressive and the radial stress on the mandrel reduced. This will then lead to an increased risk of coil collapse compared to the situation where the mandrel does not collapse. There will also be discontinuities in the mandrel pressure due to the slip-stick frictional behaviour in the mandrel mechanism. A typical set of coil internal stresses for the winding of 0.2 mm thick tinplate whose parameters are defined in Table 1 is shown in Fig. 6. The graphs include the tangential and radial stress distribution at the various stages of winding including the release of the outer wrap, mandrel collapse and cooling to a uniform

Fig. 6 - Simulated Coil Internal Stresses at Different Stages of Winding - Nominal Case for Tinplate Material


Tangential Stress (E=414 GPa) Tangential Stress (E=207 GPa) Tangential Stress (E=21 GPa) Radial Stress (E=414 GPa) Radial Stress (E=207 GPa) Radial Stress (E=21 GPa)



1 1 0.5 0.5 0


Radial Bore Stress Ratio (-)...

2 Tangential Bore Stress Ratio (-)

temperature. A logarithmic horizontal axis scale has been chosen to show the salient points of the solution more clearly. For the special case of a rigid mandrel it is instructive to calculate the tangential and radial stress at the coil bore before the mandrel is collapsed. This calculation was performed for 290 permutations of nominal strip thickness (0.2-3.0mm), material Young’s modulus (21,207,414GPa), strip roughness cla (0.22.9µm) and surface compressibility (0.20.7 MPa −1 ). Other data is defined in Table 1. The results for a dimensionless tangential and radial stress, obtained by dividing by the nominal body tension stress, were plotted in Fig. 7 as a function of the equivalent, radial Young’s modulus E * of the coil wraps.

0 0

0.5 1 1.5 2 2.5 Equivalent Radial Elastic Modulus E* (GPa)


Fig. 7 - Tangential and Radial Bore Stresses as a Function of Equivalent Radial Elastic Modulus

This modulus is the value one would measure if a stack of discs of the material were compression tested and is defined as:

illustrates the change in radial and tangential stress for the nominal case of a 0.2 mm tinplate coil.

α = λE s l o h ,

Radial Bore Stress (MPa) ...




140 12 135

10 Mandrel Diameter 400mm Radial Stress 500mm Radial Stress 600mm Radial Stress 400mm Tangential Stress 500mm Tangential Stress 600mm Tangential Stress

8 6



4 120

2 0

Tangential Bore Stress (MPa) ...


115 1





Wound Wrap (-)

Fig. 8 - Influence of Mandrel Diameter on Bore Stresses for a Rigid Mandrel

Another characteristic response of coils wound on different radius, rigid mandrels is shown in Fig. 8. The results for the radial and tangential bore stresses at the end of winding are shown for nominal mandrel diameters of 400, 500 and 600 mm. These show higher radial stresses for the larger diameter mandrels and similar tangential stresses. An important feature of coils wound after cold rolling is that they tend to have a significant temperature difference between the wraps rolled at full speed and those rolled at thread speed. During cooling, which may take in excess of 24 hours, the warmer body wraps shrink onto the cooler bore wraps and cause significant increases in the bore stresses. Fig.9




-50 10



-150 -200


Non-Cooled Tangential 10 Deg.C Tangential 50 Deg.C Tangential 90 Deg.C Tangential Non-Cooled Radial 10 Deg.C Radial 70 Deg.C Radial 90 Deg.C Radial

-250 -300 -350

4 2


0 1





Wrap (-)

Fig. 9 - Wound Stress Change During Cooling

The same calculation has been performed for a number of coils having a range of equivalent radial stiffnesses. The results have been expressed as a sensitivity of change in stress before and after cooling per unit degree of temperature difference between the coil bore and coil body. The sensitivity of the bore tangential stress and the maximum change in radial stress (some distance in from the bore) to temperature difference is presented in Fig.10. Radial Stress Temperature Sensitivity .. (MPa/Deg.C)

where α is the factor by which the Young’s modulus of the composite coil wraps is reduced from that of the base material. The dimensionless stress units were chosen since the results are essentially proportional to the winding tension. As can be seen the results fall into three separate sets of results corresponding to the three different base materials as defined by their Young’s modulus. The combination of strip thickness, roughness and surface compressibility which result in a particular equivalent radial Young’s modulus has a minor impact on the result for a specified material. This observation is extremely important since it reduces the dimensionality of the problem of designing tension strategies for a wide range of products.

Tangential Stress Distribution ..... (MPa)


Radial Stress Distribution (MPa)....

Es , (1 + α )


0.0 Radial Tangential

-0.02 -0.04






-0.10 -0.12


-0.14 -0.16


-0.18 -0.20

Tangential Bore Stress Temperature ... Sensitivity (MPa/Deg.C)

E* =

-2.5 0








Equivalent Radial Elastic Modulus E* (MPa)

Fig. 10 - Cooling Stress Sensitivity as a Function of Equivalent Radial Elastic Modulus

As the radial stiffness increases the radial stress sensitivity increases however the tangential sensitivity is nearly constant. Note that this result is independent of the mandrel since the coil is cooling after removal from the processing unit. The occurrence of cooling stresses makes the design of coil winding strategies significantly more difficult for rolling operations than for most other processes.

Influence of Mandrel Characteristics

The winding results presented in Figs.7 and 8 were for the idealised case of a rigid mandrel. In practice the forces on the mandrel are normally so high that the mandrel drum and the expansion mechanism suffer significant elastic deformations. If, as is often the case , the mandrel expansion is driven by a hydraulic cylinder with a defined maximum pressure setting, then there will be a defined pressure limit at the mandrel surface which will cause the mandrel diameter to contract until the pressure drops below the threshold. For a given mandrel mechanism inclined angle β , mandrel radius R o , hydraulic cylinder area A , maximum pressure Pm and friction coefficient µ , the following expression enables the maximum radial pressure σ rm at the bore to be calculated: ó rm =

Pm A

4 2 RoW (tanâ − ì )

The significance of the maximum collapse pressure, also called the radial pressure limit σ rm , is that this single parameter represents the key mandrel characteristic as far as the coil winding behaviour is concerned. If the calculations performed previously for a rigid mandrel are now repeated for the case of collapsing mandrels, having σ rm values of 0.3, 1.6 and 3.4 MPa, quite different results are obtained as shown in Fig. 11. Tangential Bore Stress Ratio (-)


Rigid Mandrel Max. Collapse Pressure: 3.4 MPa Max. Collapse Pressure: 1.6 MPa Max. Collapse Pressure: 0.3 MPa

2 0 -2 -4 -6 -8 -10 -12 0






Equivalent Radial Elastic Modulus E* (GPa)

Fig. 11 - Influence of Mandrel Characteristics on Bore Stresses.

The essential feature of the difference is that the tangential stress at the coil bore is more compressive and therefore the risk of tight centre coil collapse is greater. Often the tangential stress may now be compressive even before the mandrel is collapsed at the conclusion of winding the coil. Also, the radial

stress in the vicinity of the coil bore is reduced which reduces the minimum slip ratio and this increases the risk of telescoping. Mandrel design constraints can limit the maximum achievable bore radial collapse pressure however many older mills have severely underdesigned mandrels and suffer both interwrap slippage and or tight centre collapse as a result. The critical design parameter is the mandrel collapse ratio γ defined as the ratio of the maximum mandrel collapse pressure σ rm to the maximum radial pressure at the end of winding on a rigid mandrel. Based on the results presented in Fig. 7, the following expression for the mandrel collapse ratio may be derived: ó rm ã = * a / (E + b )− c T f* where a, b and c are constants. If the mandrel collapses easily, due to a low radial pressure limit and slippage occurs early in the coil, say after ten to thirty wraps, then the wraps may tighten up and the remainder of the coil may be free from further slippage but is more prone to tight centre coil collapse. Conversely, if the slippage happens further into the coil, then a weak spot is created in the form of an air gap or region of low radial pressure and this leads to dishing when the coil wall is typically above 350 mm. Some control over the location of the point of initial slippage could be achieve by dynamic variation of the mandrel hydraulic relief pressure. This is not a common practice at present. Another observation concerning mandrel behaviour is that the level of friction in the mandrel expansion mechanism can have a significant impact on the maximum collapse pressure and therefore upon the frequency of coil winding problems. The lower the friction coefficient the more mandrel shrinkage will occur. In particular it could alter the relative levels of dishing and coil collapse. It may also explain some of the time dependence of winding problem incidence.



Designing a Winding Tension Strategy

The design of a winding tension strategy can be a complex assignment when there is conflict between the demands of the upstream and downstream process and the optimum winding strategy. The design process can usually be


fh /


Tf (-)

Headend "Hardcore" Strategy

Tailend Strategy

Duration L


Tension Force Ratio T

Body Section

Enhanced Strategy (Wadsley) Basic Strategy Generic Strategy "Hardcore" Magnitude M


Body Tension * Tf

Radius Ro

0 1



Coil Wall Thickness(mm)


Fig. 12 - Dynamic Tension Profile Strategies

The tailend tension force is intended to minimise the risk of telescoping by keeping the torque on the reel constant. This is achieved by maintaining the relationship: Tf ∝

Ro , R > Ro R

where Ro is the radius where the tailend compensation starts. The function of the headend tension strategy is to prevent coil collapse and telescoping or interwrap slippage (Cozijnsen [9], Wadsley [10]). The typical headend tension strategy in Fig.12 is composed of an initial step followed by a decreasing ramp down to the body tension. Some winding operations have the ramp section without the initial step which is not a recommended practice. Other forms are possible, such as the one shown in Fig.12 proposed by Wadsley [10] however the additional benefits of the more complex form are normally small. When investigating the optimum form of profile to use it was found that the ramp

section had no benefit other than to make an orderly transition from the high tension region to the body tension. We may therefore define the “basic” simplified headend profile by two parameters; the body tension multiplier * M = T fh T f and the duration L expressed in



terms of the coil wall thickness. Sometimes the length is defined in terms of the number of wraps however the authors have found that as the nominal strip thickness changes the wall thickness is more constant in the optimum winding strategy than the number of wraps. The headend tension adjustment is commonly referred to as the “hardcore” strategy because one of its functions is to achieve a solid coil free from the soft collapse condition induced by winding with too low a tension. As will be shown later, if the optimum result is obtained from the point of view of tight centre collapse, then interwrap slippage and soft coil collapse is not normally an issue unless the mandrel has an extremely low collapse pressure σ rm . The likelihood of a given coil buckling may be inferred from the magnitude of the tangential stress at the coil bore at the conclusion of winding when the mandrel is collapsed. Typically, the wrap most likely to buckle may be 5 to 10 wraps in from the coil bore. Therefore, in designing an optimum headend hardcore strategy, the combination of the L and M parameters which results in the least compressive tangential stress at the coil bore is sought. For the idealised case of a rigid mandrel the answer is relatively easy to find by searching all the possible combinations. Fig. 13 shows this result for the nominal case and reveals that a short hardcore length and a high multiplier M gives the optimum result. 180


160 140 120 100 80 60 40 20


Head End Multiplier M


2.00 2.75

Tangential Bore Stress (MPa)

viewed as a two stage process in which the first stage is to determine the preferred body tension, acceptable for each of the upstream and downstream processes and the second stage is to design the form of dynamic tension profile adjustment needed to ensure coil stability (ie freedom from collapse and interwrap slippage). Typical issues for selecting the range of feasible body tensions were discussed previously. A generic dynamic tension profile strategy normally consists of a headend component and an optional tailend component commonly applied to coils having a large final radius (see Fig. 12).

65 70 75 50 55 60 35 40 45 20 25 30 15 5 10

Hard Core Length (mm)

Fig. 13 - Effect of Hardcore Strategy on Tangential Bore Stress for a Rigid Mandrel



Tangential Bore Stress (MPa)


Nominal Case (L=20, M=2) Hard Core Length L=5mm Hard Core Length L=15mm Multiplier M=1.5 Multiplier M=2.5 Body Tension = 35 MPa Body Tension = 105 MPa

140 120 100 80 60 40 20 0 0






Equivalent Radial Youngs Modulus E* (GPa)

Fig. 14 - Effect of Hardcore Strategy and Body Tension on Tangential Stress for Different Strip Materials and a Rigid Mandrel

The tangential stress shown in Figs. 13 and 14 is that achieved at the end of winding before the mandrel is collapsed. The interpretation of this result is that, by prestressing the inner bore wraps for a wall thickness of L and then lowering the tension for the remainder of the coil, one minimises the extent to which the winding of the body of the coil drops the initial tension towards a condition of greater compression after winding is complete. If the case of a collapsing mandrel is considered, a different and more complex picture emerges. Fig. 15 presents the wound tangential bore stress for a mandrel with a maximum collapse pressure of 3.3 MPa and similar conditions to those of Fig. 13. 0 -50 -100 -150 -200 -250 -300 -350 -400


Head End Multiplier M


Tangential Bore Stress (MPa)


-450 65 70 75 50 55 60 35 40 45 20 25 30 15 10 5

Hard Core Length (mm)

Fig. 15 - Effect of Hardcore Strategy on Tangential Bore Stress for a Controlled Collapse Mandrel

Results are presented for the nominal body tension of 70 MPa. It should also be mentioned

that, for the nominal case, a uniform strip thickness is assumed along the coil length. The need to keep the hardcore strategy “short and sharp” is evident. For tinplate rolling as little as 50 wraps may be adequate to achieve the desired result. The negative impact of long hardcore lengths is clearly shown. The previous discussion might be interpreted as suggesting that not much benefit is gained from the hardcore as far as the tangential stress is concerned. The simulation results presented previously were for a coil with a constant thickness along its length. This is a good assumption for many processing operations and for continuous rolling mills which have short transition lengths between orders. It is not justified for conventional batch operation cold rolling mills where there is a significant length of thick material on the head end of the coil. In tinplate rolling the initial thickness may be 300 percent thicker than nominal and it may require 100m of strip to be rolled before the thickness is close to the nominal value. There are several consequences arising from this situation: • the winding tension stress is lowered in the critical head end region in proportion to the amount by which the thickness is increased. • the effect of the thickness profile changes the tangential bore stress dependence on the hardcore parameters in a favourable manner as revealed in Fig. 16. 0 Tangential Bore Stress (MPa)

A set of results for different body tensions and a range of equivalent radial elastic moduli suggests that the optimum combination of L and M is independent of E* (Fig. 14).





-150 -200 -250 -300 -350 -400 1.25



5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

2.25 2.75

Head End Multiplier M

Hard Core Length (mm)

Fig. 16a - Effect of Hardcore Strategy on Tangential Bore Stress for a Controlled Collapse Mandrel When a Headend Thickness Profile is Present Before Mandrel Collapse

Collapsed Tangential Bore Stress (MPa)

0 -50




-150 -200 -250 -300 -350 1.25 1.75

-400 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

2.25 2.75

Head End Multiplier M

Hard Core Length (mm)

Fig. 16b - Effect of Hardcore Strategy on Tangential Bore Stress for a Controlled Collapse Mandrel When a Headend Thickness Profile is Present After Mandrel Collapse

the thicker strip at the coil bore has a major effect on the compressive stress that can be supported before buckling occurs since the dependence is on thickness squared. • by deliberately rolling a controlled amount of thicker material at the head end of a coil an additional avenue for coil collapse control is introduced. Figure 16 has two 3-D plots representing the tangential stress before and after the mandrel is collapsed for the case where there is an initial headend thickness increase of 240 percent tapering to zero after approximately 60m. This enables a comparison to be made with the result of Fig. 15, which was for the condition before the mandrel was collapsed. The preferred strategy is still to keep the duration of the hardcore strategy short. Usually there are practical issues which limit the minimum hardcore wall thickness to approximately 10mm. Three-Dimensional Effects

When a coil of strip having an appreciable thickness profile is wound, there are several important consequences which arise:

the diameter of the coil is greater on the mill centreline than at the strip edges. • the transverse stress distribution in the strip as it approaches the initial coil contact becomes increasingly non-uniform. • the general shape of the transverse strip tension profile is similar to the surface profile of the coil (ie the diameter distribution). • the radial and tangential stress distribution at the coil bore will vary across the strip width as a result of the non-uniform winding tension at different points across the strip width. • if the stresses in the strip at any stage exceed the material yield stress in plane stress, then plastic yielding may occur. This effect is most significant for softer materials such as aluminium foil and temper rolled steel. The consequence for coil winding is that at some point across the strip width in the coil bore region there will be a more compressive tangential stress which will increase the risk of coil collapse. This risk is compounded if there is manifest bad shape introducing buckled strip onto the wound coil near the coil bore. Another source of stress variation across the strip width can arise from shape stress variations due to poor flatness and these are typically less than 50 MPa from the mean stress. The influence of these flatness errors was found to be small compared to the thickness profile effect. For the nominal case of rolled strip having a thickness and width of 0.2mm and 1000mm respectively, the buildup of the radial and tangential stress distribution through the coil has been calculated at different locations in the coil for the condition existing at the end of winding (See Fig. 17).


0.2 3 6 13 32 81 240 596

100 80 60



Radial Stress (MPa)

Tangential Stress (MPa)




40 20 0

50 40









30 20

-20 10 -40 0

-60 -1.5







Dimensionless Distance From Coil Centre Line (-)








Dimensionless Distance From Coil Centre Line (-)

a) Transverse Tangential Stress Distribution

b) Transverse Radial Stress Distribution

Fig.17 - Axi-Symmetric Stress Distribution Through Wound Coil Having a 3.0 Percent Transverse Thickness Profile

The simulation results show firstly that the thickness profile increased the difference between the centre and edge region tangential stresses at the bore. Another feature of this distribution was that after approximately 10 wraps, the stress in the edge zone went to zero due to the thickness profile effect. Monitoring the Winding Process

The monitoring of winding operations is often hampered by the lack of instrumentation and reliable coil observations. Audits of coils in a storage yard for the frequency and severity of presentation defects is often a good starting point. Correlating the defect frequency with product dimensions and tension strategies may provide guidance as to where the problem may be originating. Ideally, the following winding parameters should be recorded dynamically for each coil: tension force, strip thickness, mandrel hydraulic pressure and mandrel expansion shaft movement. It is also extremely useful if a slippage detector can be installed to identify when interwrap slip is occurring. These parameters can be used to tune a coil winding simulation model to match what is observed and then to iteratively search for an optimum operating point which minimises winding problems. If that is not satisfactory then a redesign of the mandrel may be necessary, usually to increase the mandrel pressure at which collapse is initiated. It is also worthwhile to keep track of all mandrel maintenance and lubrication activities as it can be the case that supposedly innocent changes can trigger a spate of winding problems.


Illustrations of the benefits of optimising the winding strategies or process equipment to minimise winding problems are: A tandem mill rolling tinplate was experiencing a higher than desired incidence of tight centre coil collapse. By the single change of reducing the hardcore length by a factor of approximately 50 percent, the frequency of collapse was reduced by a factor of 5. Another tinmill had extreme combinations of telescoping and tight centre and soft coil collapse on 10 percent of the product. These problems were reduced by a factor of 4 by introducing a “short and sharp” hardcore strategy. In this case the mandrel maximum collapse pressure was below 0.5 MPa and needed to be improved by a redesign to cure the remaining coil winding problems after the hardcore was optimised. Two tinmills which had optimised hardcore strategies still had unacceptable collapse histories until a deliberate thickening of the headend was introduced. This did not increase the length of out of tolerance material although there was a small yield impact which was more than compensated by the elimination of collapsed coils. A steel sheet mill operation was found to have a plethora of mechanical issues on each of its process operations from pickling through to the exit of metal coating. In this case a methodical elimination of alignment problems, steering instabilities, worn belt wrapper equipment, loose

guide boxes and improved winding tension strategies was needed. • A steel temper mill observed bad flatness in the final coil that was not measured by the shapemeter. The cause was found to be plastic yielding in the centre section of the coil triggered by a combination of transverse thickness profile and an excessive body winding tension. The defect was eliminated by lowering the winding tension. Each particular situation had to be investigated individually as there is no one solution to suit all problems.

winding on controlled collapsed mandrels. While useful, simulation models are not perfect and the caution of Albert Einstein should be kept in mind: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they don’t refer to reality.” References 1.




The preceding discussion of the mysteries of coil winding was intended to highlight the physical phenomena which determine coiling behaviour and the types of remedial action which may be relevant to a particular type of winding defect. The interactions between tension strategies, mandrel deformations and internal coil stress distributions are complex and practical problem solving is hampered by the lack of relevant measurements. As in most fields of process engineering, many problems arise from poor maintenance and a failure to appreciate the criticality of key equipment components and operating strategies. Simulation models have been used extensively to gain insight into the characteristics of coil


5. 6. 7.

8. 9.


Chen K and Wang Z-C, ' Investigation of Buckling of Coiled Strip under High Winding Tension', Iron and Steel, (China) 24(11), (in Chinese), pp.34-38, 1989. Goodridge R J, 'Reel Drives for High Performance Rolling Mills and Metal Processing', GEC-AEI Journal, Vol.35, No.1, 1968. Sims R B and Place J A, 'The Stresses in the Reels of Cold Reduction Mills', J. Applied Physics, Vol.4, pp 213. 1953. Wilkening H, Doctoral Thesis 'Determination of the Radial Coiler Loading During the Coiling of Strip', RheinischWestf¬lischen Technischen Hochschule, Aachen, 1965. Altmann H C, 'Formulas for Computing the Stresses in Centre-Wound Rolls', Tappi Journal, 5(4), 1968, pp 176-179. Wadsley A W and Edwards W J, 'Coil Winding Stresses', J. Australian Institute of Metals, Vol.22, pp 17-27, 1977. Yuen W Y D and Cozijnsen M, 'Optimum Tension Profiles to Prevent Coil Collapse', SEAISI 2000 Conference Vol.2, Perth, May 2000. Turley J W, 'Sendzimir Controlled Collapse Winder', Iron and Steel Engineer Vol.51, No.42, November 1974. Cozijnsen M and Yuen W Y D, 'Stress Distributions in Wound Coils', 2nd Biennial Australian Engineering Mathematics Conference, Sydney, pp 117-174, 1996. Wadsley A W and Edward W J, 'Note on Coil Winding Investigation of Tight Centre Coil Collapse', Australasian Institute of Metals, 30th Annual Conference, Newcastle, May 1977.


Winding tension force

Nomenclature A

Area of mandrel expand cylinder


Young’s modulus of base strip material

Tf*,Ts *

Nominal winding tension force, stress


Equivalent Young’s Modulus in the radial direction


Bending component of tension


Strip thickness


Inertia component of tension


Motor armature current


Strip speed

Polar moment of inertia of motor, mandrel and coil


Motor armature voltage

lo ,l

No load, loaded separation of rough surfaces in


Strip width

contact L

Hardcore wall thickness


Critical buckling length


Wall thickness


Hardcore headend tension force ratio


Maximum hydraulic pressure in mandrel expand mechanism


Radial location of point within a coil


Coil outer radius


Material yield stress


Mandrel nominal radius


Electric energy conversion efficiency


α β γ λ

µ σr ,σt σ rm

Young's Modulus ratio with respect to base material Mandrel mechanism angle Mandrel collapse ratio Rough surface compressibility Coefficient of static friction is mandrel mechanism Radial, tangential stress Maximum mandrel collapse pressure at coil bore

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