Robust Reference Tension Optimization in Winding Systems Using Wound Internal Stress Calculation

Transcription

1 01 AIMCAL Europe and USA Web Coating Conference & Web Handling Conference Robust Reference Tension Optimization in Winding Systems Using Wound Internal Stress Calculation By 1 M hamed Boutaous & Patrick Bourgin CETHIL, INSA Lyon - France Mhamed.boutaous@insa-lyon.fr Dominique Knittel Université de Strasbourg, France

2 OUTLINE Introduction Optimization of the winding tension - Offline optimization - Online optimization Influence of the dynamic gauge Effect of the reference tension variations rate Optimization of the admissible tension dispersion Conclusion

3 Introduction : Winding flexible media Main defects - Wrinkles, - Interlayer slipping, - Waviness Why? - Technology or Process (geometry, design, tension, winding velocity, nip force,...) - Product (mechanical properties, surface topography ) Challenge in winding : good quality rolls. Mathematical models of the stress within the roll. The role of the TENSION REFERENCE in stress state. 3 New proposal: control the tension in terms of computed internal stress

4 Role of the tension reference Influence of the nominal tension on the stress components. Stress Winding tension (Kg) Stress 8 x Tangentiel stress Radius Radius Effect of tension fluctuation.

5 Optimization of the winding tension J Optimum reference tension = industrial know-how. Model of stress computation Criterion J The reference tension which minimizes criterion J is optimized using an algorithm based on the principle of the simplex (Nelder and Mead, 1965). R = max R roll (σ θ (T w ) σ θmean (r)) g(σ θ,r)) dr 10 x 10 Tangential stresses and stress gauge g (σ θ, r) weight function defined by : 9 8 g (σ θ, r) = 1 if is in the gauge g (σ θ, r) >>1 if else. Stress (Pa) (a) (b) Normalized Radius 5 Optimization gauge for tangential stress

6 Offline optimization of the reference tension Distributed control: Sensorless measurement of the tension with control based on fuzzy logics and neuronal networks.(ex: Wolfermann.) Offline optimization of the reference tension - No perfect follow-up of the instruction - Fluctuations due to the imperfections of the winding chain. - Induced variations of the stress within the roll, as compared with the one which would result from an ideal control. NEED TO MODIFY THE REFERENCE TENSION AFTER EACH LAYER: A NEW CONCEPT 6

7 Online optimization of the reference tension Winding tension reference Winding Tension of the global wound J R = max ( σ ( T ) σ ( r)) g( σ, r)) dr R roll w mean Pack 1... Pack i measured tension Corrector Winding Plant Pack 1... Pack i measures g (σ, r) weight function : g (σ, r) = 1 if σ is in the gauge g (σ, r) >>1 if else. J= min (J T, J R ) Pack i+1... Pack n Radius Prediction algorithm Stress gauge Predictions Pack i+1... Pack n Computation of stress state Computation and minimization of J Principle: The reference tension is modified (adjusted) layer after layer according to the criterion J At time ti, which corresponds to the winding of pack i. Packs 1 to i-1 are already wound: we know their tension reference and their actual values (measured). The instruction for i is also clearly defined and it is now, possible to calculate the instruction from i+1 to N, then to compare the values of the tension measured with the ones predicted by the model for a fictive roll. By the gauge of the tangential stress, we will calculate the weight function. The optimization of this function by minimizing it according to the principle of the simplex makes it possible to find the optimal online tension reference for the remainder of the roll: i+1 to N. The next instructions will be thus updated as the roll is being wound. 7

8 Examples: Comparison Winding web tension Online measurements Winding web tension Prediction of the reference tension Offline On / Off Initial tension Final tension : Time t i Tf on Tf off Offline optimized reference tension Pack 1 Radius Pack Pack i Pack i+1 Pack n Offline and online reference tension 8 Dividing the roll radius into several segments, the tension reference is computed and corrected for each range of roll radius values, by using the predictive model for the stress within the roll. The adjusted tension is updated step by step, following the optimization principle as described above and it will be considered as the new tension reference value for the coming layers

9 Examples: Control with simulated noise in tension measurement (Constant gauge) 8 x 10 Curve Offline, real and optimized control tension with random noise Radial stresses 3 1 Curve The tangential stresses are more affected than the radial stresses - The perturbation affects only the wound part, but not the remainder part Tangential stress at several time during the winding process 9

10 local perturbation and constant gauge - Before the perturbation, the offline and the online tensions are the same. - We observe the different steps of the online optimization 10

11 Effect of a dynamic gauge The gauge is fixed during all the process of winding for the offline optimization. Periodic disturbance in the reference tension Corresponding radial and tangential stresses The gauge is assumed 10 times higher from the pack N 0 to 55 for the online one, for both the radial and the tangential stresses. 11

12 Effect of a dynamic gauge The gauge is fixed during all the process of winding for the offline optimization, Periodic disturbances in the reference tension The gauge is assumed 10 times higher from the pack N 0 to 55 in the online one but just for the radial stresses. Corresponding radial and tangential stresses 1 The result is that the tangential stresses in the central zone are lower compared to the precedent case.

13 Effect of a dynamic gauge Corresponding radial and tangential stresses Periodic disturbance in the reference tension The gauge is assumed 10 times lower from the pack of layers N 0 to 55 in the online one but just for the radial stresses. 13 For example, in the case of risk to have negative tangential stresses, this optimization is a way to prevent it.

14 Maximum Reference Tension Gauge? T max? and T min? such as T min < T ref < T max σ (T ref ) located between fixed stress gauge Problem to solve: T ref +/- C: C maximum =? T ref T max C can also be C(r) T min C=? 1

15 Effect of the reference tension variations rate during winding The control of winding systems is generally based on practical experience and the tension reference does not change or decreases according to a more or less complicated function of the radius. The optimum tension is that which guarantees that the stresses within the roll still confined in a desired gauge The practical question is to know the limits of variations of the reference tension, i. e. witch slope of decreasing to impose to the reference tension without exceeding prescribed stresses values. 10 x T decreases from 18 to N: Tmin T decreases from 0 to 6 N: T max T decreases from 18 to 6 N: T T decreases from 0 to N: T1 Tangential stresses ( Pa) Layers number

16 Effect of the reference tension variations rate during winding In the precedent figures, surprisingly, the obtained results are different from that expected. Indeed, the stresses σ(t 1 ) calculated with T 1 as reference, is not confined between σ( T max ) and σ( T min ). The same observation has been made for tangential stresses σ(t ) computed with T as reference tension. Conclusion: The slope of the reference tension influences the stresses as well as the tension value itself. The magnitude of the tension is a key parameter, but not sufficient. The rate of the tension decrease plays an important role too. 16

17 Effect of the fluctuations with maximum slope around the reference tension Consider now the extreme case: T varies alternatively, with a maximum slope, between T max and T min : for each new wound layer, T passes alternatively from T max to T min. Hence, the applied reference tension, named T alt is given by T alt = (a.r +b) +/- c (curves in the figure below are given with c = 1 or ) 1.8 x 105 T varies alternatively between Tmax and Tmin Tension (N) Layers Number Alternative variations of the tension between maximal and minimal values

18 Effect of the fluctuations with maximum slope around the reference tension Tangential Stresses (Pa) 10 x T decreases from 18 to N T decreases from 0 to 6N T = (a* r+b ) +/- 1 T = (a* r+b ) +/- 1- Any reference tension which lies between T min (r) and T max (r) gives stresses with values confined between those calculated for a tension which varies alternatively between T min (r) and T max (r) Layers number - If the dispersion (T max (r) - T min (r) ) is too large, the stresses can overcross their gauge, and one risks to have defects in the roll. It is thus important to calculate this authorized maximum dispersion. 18

19 Effect of the fluctuations with maximum slope around the reference tension If the fluctuations become more and more (or less and less) important with the radius. The parameter c becomes function of the radius, and the reference tension presents an attenuation (or an exaggeration) of its fluctuations during winding. Reference Tension (N) x 105 Tw = (a*r +b)+-c c increases with the radius r c decreases with the radius r Layers Number Radial stresses (Pa) Tangential stresses (Pa) 0 x 10 Radial Stresses x 10 Tangential Stresses 5 c increasing with the radius c decreasing with the radius c increasing with the radius c decreasing with the radius Layers Number The stresses remain globally comparable. But the risk of web wrinkling due to negative tangential stresses, when the fluctuation decreases (triangle symbols), is more important than in the inverse case (circle symbols). The same phenomena is confirmed when the roll radius is more important. 19

20 Effect of the fluctuations with maximum slope around the reference tension Radial stresses (Pa) x 105 Radial stresses c decreases with the radius c increases with the radius r Tangential stresses (Pa) 8 x 105 Tangential stresses Layers Number c decreases with the radius r lower limit of the gauge c increases with the radius r 0 The same phenomena is confirmed when the roll radius is more important.

21 Optimization of the ADMISSIBLE TENSION DISPERSION Tref = ar + b ± C The maximum value for C (admissible dispersion) is obtained by minimization of the criterion J using the simplex optimization algorithm (Nelder and Mean 1967) J = ( σ σ ( T )) g( σ ) g (σ θ ) weight function defined by : g (σ θ ) = 1 if θ critical θ ref θ σ σ σ θmin θ( T ref ) θmax g (σ θ ) >>1 else 1

22 Optimization of the ADMISSIBLE TENSION DISPERSION C is choosen constant 9 Optimized winding tension 8 7 Tension (N) x 10 Optimized tangential stresses Number of layers C = Tangential stresses (Pa) Number of layers

23 Optimization of the ADMISSIBLE TENSION DISPERSION C can be C (r) C (r) = α r + β α =?, β =? 9 Optimized winding tension 8 Tension (N) Number of layers Tangential stresses (Pa) x 10 Optimized tangential stresses 5 3 C(r) max = Number of layers

24 CONCLUSION -Well-known observation: the winding tension strongly affects the roll internal stress. -BASIC IDEA: control the tension with respect to the stress generated within a roll. -NEW CONCEPT: ONLINE ADAPTATION OF THE REFERENCE TENSION -The new optimization strategy called online optimization associated with a dynamic gauge is used and compared to the classical offline one. The comparison shows interesting improvements, in providing an internal stress state compatible with elastic deformations of the web within the roll. -A second approach consists to optimize the tension reference gauge in order to make the choice of the winding reference confined in a constraining gauge, with respect to the stress state within the roll.

25 CONCLUSION Two applications can be aimed by this approach: - the estimation of the dispersions of the measured tension with regard to the reference one, let to deduce if the wound roll stress state respects the stress gauge, without recalculating the stresses. - for a defined stress gauge, one can calculate the reference tension gauge, with respect to the stress state within the roll. By defining au Stress Gauge We estimate the T ref max (T ref optimal or not) 5