Modeling & Analysis of a Printing Line Coating Section

APPLIED INDUSTRIAL CONTROL SOLUTIONS
ApICS LLC.

Analysis of a Printing Line

Coating Section

Brian T. Boulter

ABSTRACT

This report details the modeling, simulation and resulting control scheme and mechanical configuration recommendations for a coating section installed by a third party printing OEM.

INTRODUCTION

Scope

This engineering report describes the modeling and simulation of an in-line coating section installed by a third part printing equipment manufacturer at an installation.

Objective

An adequately detailed model of the coater was developed. The purpose of the modeling and investigation was to observe the effect of backlash on the observed registration error in the coater, with the existing control scheme. In addition, several alternative control schemes were to be investigated, and the results presented in the following SR.

Report Overview

The report is divided into four sections. The first chapter defines a set of useful terms, and the governing first principal equations; the second describes the simulation structure. The third chapter presents the conclusions, and finally the fourth chapter presents a set of recommendations.

CHAPTER 1

FIRST PRINCIPAL EQUATIONS

Introduction

The equations describing the dynamics of this type of system have been described in detail in the engineering course "Advanced Dynamic Simulation". The following descriptions are only brief and are not intended to describe every detail of the simulation. The derivation of all the equations used to describe the dynamics of the described system, can be also be found in the same course material.

Nomenclature:

J_i,_M	The i’th motor inertia [lb ft^2]
J_i	The i’th reflected roll (load) inertia [lb ft^2]
V_i	The i’th roll surface velocity [ft/min]
w_i,m	The i'th motor rotational velocity feedback [rpm]
w_I	The i'th roll rotational velocity feedback [rpm]
B_V	Viscous friction [lb ft sec / rad]
B_W	Square-law windage friction [lb ft sec^2 / rad]
B_C	Coulomb friction force [lb ft sec / rad]
B_S	Stiction friction force [lb ft sec / rad]
wr_i	The i'th motor rotational velocity reference [rpm]
w_SMLi	The i'th SML bandwidth [rad/sec]
w_CCLi	The i'th CCL bandwidth [rad/sec] (outer loop)
w_Si	The i'th speed-loop PI lead freq. [rad/sec]
K_Si	The i'th speed-loop PI prop. gain
w_Ci	The i'th cascaded outer-loop PI lead freq. [rad/sec]
K_Ci	The i'th cascaded outer-loop PI prop. gain
R_i	The i’th roll radius [ft]
GR_i	The i’th roll gear ratio
L_i	The i’th tension zone length [ft]
T	The i’th tension zone tension [lb]
t	The i’th roll reflected shaft torque [lb ft]
	The i’th motor maximum torque [lb ft]
E_i	Strip modulus of elasticity [PSI]
A_i	Strip cross sectional area [in^2]
s	The Laplace operator
J_i	J_MOTOR+ J_LOAD Reflected Inertia [lb ft^2]
K_SP,i	The i’th shaft torque/deflection curve gain constant [lb ft/rad]
K_D,i	The material damping co-efficient [lb sec / ft]

System Description:

The system that is modeled in the simulation is shown in Figure 1-1. The printing process chill section is modeled as an ideal speed/tension source. The exit of the coater chill section is modeled as an ideal tension sink. A simplified diagram of the system is presented in Figure 1-2. The simplified system representation is described with the same nomenclature that is used in the first principal equations.

All radii, inertias, gear ratios, and other physical properties relating to the modeled plant used in the simulation are subscripted with the following symbols:

Impression Roll	IR	Impression Roll Motor	IR,M
Blanket Roll	BR	Blanket Roll Motor	BR,M
Anulux Roll	AR
Chill Roll	CR	Chill Roll Motor	CR,M

Figure 1-1. Coater System

Figure 1-2. Simplified Coater System Representation

The web spans in the process are computed as the lengths of free web spanned in the section. The inertias used in the simulation were calculated based on a combination of information supplied by the OEM, and a-priori knowledge of typical inertias for these types of systems. All information pertaining to gear ratios, diameters, radii, and free span lengths were supplied by the OEM.

Shaft spring constants were computed based on a-priori knowledge of typical natural frequencies for these types of mechanical systems. Similarly, guesses were made with respect to gear-box damping of higher order resonant modes, and the properties of material damping associated with the conveyance of cardboard material through this type of processing equipment. The values typically used for hard Kraft paper were used in this case.

The investigation of the effect of backlash in the gear-box was accomplished with best guesses about the typical backlash found in the gear-boxes on-site.

Describing Equations:

The following equations describing the dynamics of the modeled system are divided into two parts. The first section deals with equations describing the drive trains, and the coupling of the Impression, Blanket, and Anulux rolls. The second section presents the equations describing the conveyance of web in processing lines.

A separate section describes the controllers, and the theory used in tuning them.

Drive Train Equations:

The equations describing the dynamics of the drive train are non-linear in nature. To assist in the description of these non-linear equations a linearized model is first described, then the modifications to the linearized model are presented with an explanation and supporting diagrams.

; (1.1)

where the loss torque is a non-linear contribution that is a function of the magnitude and direction of the shaft speed. Equation (1.2) is a popular model that adequately represents the non-linear aspects of friction. It is from standard tribology texts on the subject.

(1.2)

Figure 1-3. Graph of Typical Loss Torque shown in (1.2)

For applications where a drive train model is not needed the above description is adequate, however in this analysis, a representation of the drive train dynamics was required, in order that the dynamics associated with gear backlash could be included in the investigation. To model gear backlash the above differential equation must differentiated one more time to represent the system in terms of rotational displacement, rather than speed. This is because a representation of backlash is defined in terms of a zero change in torque, for a given change in shaft displacement, as shown in Figure 1-4. This figure shows the "hysteresis region" or the "backlash" region, where a relative large change in shaft displacement produces little or no change in shaft torque.

Figure 1-4. Graph of Typical shaft/gear-box Torque/deflection Curve

The linearized equations describing the relationship between shaft position, shaft torque and inertai acceleration, can be found in CH 2 and 3 of the E0108 "Fundamentals of Advanced Dynamic Simulation" course material. They are summarized below:

; (1.3a)

; (1.3b)

The model should implemented in such a way that dead-band in the torque/deflection curve is included (using a dead-band block)

Coupling between sections is accomplished with gain scheduled terms that link output power from one section to the input power of the coupled section, and visa-versa.

Web Transport Equations:

The equations describing the transport of web material through the process have also been derived and explained in detail in CH 4 of the E0108 "Fundamentals of Advanced Dynamic Simulation" course material. They are summarized below:

; (1.4)

where:

(1.5)

The addition of material damping is accomplished as follows:

; (1.6)

CHAPTER 2

SIMULATION STRUCTURE

Figure 2-1. Simulation Main Block Diagram

Main block diagram description

The main block diagram contains the main sub-systems of the simulation: The Control sub-system, which contains the controllers, and the Plant sub-system, which contains the model of the coater and web dynamics.

A set of monitoring scopes and variable file generation blocks are also included, along with the S-Curve blocks for ramping the speed reference, and tension references.

Figure 2-2. CONTROL Main Block Diagram

CONTROL block diagram description

The CONTROL sub-system block diagram contains the separate controller sub-systems. Each controller is modelled with SIMULINK ™ S-Functions that are built with the same difference equations used in the drive. They include models simulating sample time, trasport delay, and round-off errors. The driven sections that are modeled in the simulation are the three speed loops (Impression, Blanket, and Chill-Roll), along with the position and tension loops.

Figure 2-3. IMPRESSION SPEED Main Block Diagram

IMPRESSION SPEED block diagram description

The IMPRESSION SPEED loop is modeled with a simple PI, a limit, and an optional lead/lag in the feedback. This closely models the discrete behavior of the configurable drive speed loop. Inertia compensation was accomplished with a diff/lag feeding the additional torque reference forward based on speed reference.

The gains and frequency tunable values used in the simulation were the same as those used on-site. The sample time used for the discrete models was 20 [msec].

Figure 2-4. BLANKET SPEED Main Block Diagram

BLANKET SPEED block diagram description

The BLANKET SPEED loop is also modeled with a simple PI, a limit, and an optional lead/lag in the feedback (L/L shown disconnected). This closely models the discrete behavior of the configurable drive speed loop. Inertia compensation was accomplished with a diff/lag feeding the additional torque reference forward based on speed reference.

The gains and frequency tunable values used in the simulation were the same as those used on-site. The sample time used for the discrete models was 20 [msec].

Figure 2-5. CHILL-ROLL SPEED Main Block Diagram

CHILL-ROLL SPEED block diagram description

The CHILL-ROLL SPEED loop is also modeled with a simple PI, a limit, and an optional lead/lag in the feedback (L/L shown connected). This closely models the discrete behavior of the configurable drive speed loop. Inertia compensation was accomplished with a diff/lag feeding the additional torque reference forward based on speed reference.

The gains and frequency tunable values used in the simulation were the same as those used on-site. The sample time used for the discrete models was 20 [msec].

Figure 2-6. POSITION BLANKET Main Block Diagram

POSITION BLANKET position regulator block diagram description

The POSITION BLANKET loop is also modeled with a simple PI, a limit, and an optional lead/lag in the feedback (L/L shown disconnected). This model was altered to closely model the discrete behavior of the configurable position loop.

It should be pointed out that the position regulator that is being used on-site does not use any integral gain. It was found through simulation that the settling time of the position regulator (used for electronic line-shaft control) was too long, so integral gain was used in the simulation. A lead/lag was also implemented in the feedback of the position loop to investigate the usefulness of feedback forcing.

The gains and frequency tunable values used in the simulation were implemented to closely reflect those used on-site. The sample time used for the discrete models was 2 [msec].

Figure 2-7. TENSION CHILL Main Block Diagram

TENSION CHILL tension regulator block diagram description

The TENSION CHILL loop is also modeled with a simple PI, and a limit. The PI was modeled to closely simulate the drive outer trim loop.

The gains and frequency tunable values used in the simulation were implemented to closely reflect those used on-site. The sample time used for the discrete models was 20 [msec].

Figure 2-8. PLANT Main Block Diagram

PLANT block diagram description

The PLANT sub-system contains the SIMULINK ™ implementations of the first-principal describing equations for the simulation. The PLANT sub-system is divided into three main parts. A sub-system describing the dynamics of the Impression/Blanket/Anulux roll mechanics, a sub-system describing the dynamics of the Chill-roll mechanics, and a sub-system describing the dynamics of the Web material.

The web dynamic model assumes that the material has some visco-elastic damping (Cardboard has a high amount of material damping, for the purpose of simulation the web-material was modeled using Kraft paper models, given that Kraft paper does not have as much material damping as cardboard, the simulation can be considered a worst-case scenario).

Several monitor tap points are included for feeding tension, surface speed, and torque information back to the MATLAB ™ workspace for plotting.

Figure 2-9. IMPRESSION ROLL Main Block Diagram

IMPRESSION ROLL block diagram description

The IMPRESSION ROLL sub-system is composed of three main sub-systems: A model of the impression roll dynamics, a model of the Blanket roll dynamics, and a model of the Anulux roll dynamics. Coupling between the physical elements is included.

Note that a crude registration controller is included. It is a simple Integrator, that is tuned to correct for the registration error between the impression roll surface speed and the Blanket roll surface speed . It was included in the simulation to quicken the convergence of the registration thereby shortening the simulation time to 20 [sec] (20 [sec] of simulation time takes approx. 12 [hours] of computing time, so it was necessary to include some time-saving additions to the simulation)

Figure 2-10. IMPRESSION ROLL Sub-system Block Diagram

IMPRESSION ROLL Sub-system block diagram description

The IMPRESSION ROLL sub-system is a two mass model. The model includes motor inertia, impression roll inertia, backlash (i.e. deadband in the gear box), viscous friction (on the load roll), and a simple gear-box damping model (for damping high frequency vibration modes). A coupling gain term (set at 10%) is included to model the coupling between the impression roll and the blanket roll through the printed material.

Figure 2-11. BLANKET ROLL Sub-system Block Diagram

BLANKET ROLL Sub-system block diagram description

The BLANKET ROLL sub-system is also a two mass model. The model includes blanket roll motor inertia, blanket roll inertia, backlash (i.e. deadband in the gear box), viscous friction (on the blanket roll), and a simple gear-box damping model (for damping high frequency vibration modes). A coupling gain term (set at 50%) is included to model the coupling between the anulux roll and the blanket roll through the coating material.

Figure 2-12. ANULUX ROLL Sub-system Block Diagram

ANULUX ROLL Sub-system block diagram description

The ANULUX ROLL sub-system is also a single mass model. The model includes anulux roll inertia, backlash (i.e. deadband in the gear train between the blanket roll, and the anulux roll), viscous friction (on the anulux roll), A coupling gain term (set at 50%) is included to model the coupling between the anulux roll and the blanket roll through the coating material.

Figure 2-12. CHILL ROLL Sub-system Block Diagram

CHILL ROLL block diagram description

The CHILL ROLL sub-system is also a two mass model. The model includes chill roll motor inertia, chill roll inertia (the lumped inertia of all the driven chill rolls), backlash (i.e. deadband in the gear box), viscous friction (on the chill roll), and a simple gear-box damping model (for damping high frequency vibration modes).

Figure 2-13. WEB Sub-system Block Diagram

WEB block diagram description

The WEB sub-system is also a two tension zone model. It reflects a SIMULINK ™ implementation of the web mass flow equations described in Chapter 1. Material damping has been included, the parameters used to initialize the model reflect those used for heavy Kraft paper.

CHAPTER 3

RESULTS

Introduction

The sets of plots following this introduction are presented in sub-sets each comprised of five plots. The five plots are:

Registration error: A plot of the difference between the ideal blanket roll and impression roll surface alignment and the actual alignment.
Position error: A plot of the difference between the ideal electronic line-shaft synchronized position, and the actual position.
Tensions: Plots of the tensions, T₁ and T₂.
Torques: Plots of the shaft torques for the Impression roll, Blanket roll, and Chill roll motors (at the motor).
Surface Speeds: Plots of the Impression roll, Blanket roll, and Chill roll surface speeds.

Simulation runs were made with backlash in the drive-trains, and without backlash in the drive trains. For simulations that included backlash in the drive trains, the following amounts of backlash (at the motor shaft) were included:

Impression Roll: 1 [deg]

Blanket Roll: 2 [deg]

Anulux Roll: 2 [deg]

Chill Roll: 5 [deg]

A script file that describes the intialization of the simulation is included in Appendix A. For each test run, a test*.mat data file was saved, for the purpose of recovering simulation data at a later date.

Set-up Summary

The following set-ups were investigated:

A set of plots with the Impression Roll Speed Loop included, and no lead/lag in the impression roll, Blanket roll, or Chill roll speed loop feedbacks. With backlash. (Figures 1 – 5)
A set of plots with the Impression Roll Speed Loop included, and no lead/lag in the impression roll, Blanket roll, or Chill roll speed loop feedbacks. Without backlash (Figures 6 – 10)
A set of plots without the Impression Roll Speed Loop included (i.e. impression roll running as a torque regulator), and no lead/lag in the impression roll, Blanket roll, or Chill roll speed loop feedbacks. With backlash. (Figures 11 – 15)
A set of plots without the Impression Roll Speed Loop included (i.e. impression roll running as a torque regulator), and no lead/lag in the impression roll, Blanket roll, or Chill roll speed loop feedbacks. Without backlash. (Figures 16 – 20)
A set of plots without the Impression Roll Speed Loop included (i.e. impression roll running as a torque regulator), and no lead/lag in the impression roll, or Chill roll speed loop feedbacks, with a lead/lag in the Blanket roll speed feedback. With backlash. (Figures 21 – 25)
A set of plots without the Impression Roll Speed Loop included (i.e. impression roll running as a torque regulator), and no lead/lag in the impression roll, or Chill roll speed loop feedbacks, with a lead/lag in the Blanket roll speed feedback. Without backlash. (Figures 26 – 30)
A set of plots with the Impression Roll Speed Loop included, with a lead/lag in the impression roll, and Blanket roll speed loop feedbacks, no lead/lag in the Chill roll speed feedback. With backlash. (Figures 31 – 35)
A set of plots with the Impression Roll Speed Loop included, with a lead/lag in the impression roll, and Blanket roll speed loop feedbacks, no lead/lag in the Chill roll speed feedback. Without backlash (Figures 36 – 40)
A set of plots with the Impression Roll Speed Loop included, with a lead/lag in the impression roll, Blanket roll and Chill roll speed loop feedbacks. With backlash. (Figures 41 – 45)
A set of plots with the Impression Roll Speed Loop included, with a lead/lag in the impression roll, Blanket roll and Chill roll speed loop feedbacks. Without backlash (Figures 46 – 50)
A set of plots without the Impression Roll Speed Loop included (i.e. impression roll running as a torque regulator), with a lead/lag in the Chill roll and Blanket roll speed loop feedbacks. With backlash. (Figures 51 – 55)
A set of plots without the Impression Roll Speed Loop included (i.e. impression roll running as a torque regulator), with a lead/lag in the Chill roll and Blanket roll speed loop feedbacks. Without backlash. (Figures 56 – 60)
A set of plots without the Impression Roll Speed Loop included (i.e. impression roll running as a torque regulator), with a lead/lag in the Chill roll speed loop feedback, and no lead/lag in the Blanket roll speed loop feedback. With backlash. (Figures 61 – 65)
A set of plots without the Impression Roll Speed Loop included (i.e. impression roll running as a torque regulator with a lead/lag in the Chill roll speed loop feedback, and no lead/lag in the Blanket roll speed loop feedback. Without backlash. (Figures 66 – 70)

Set (1):

Plots for test1.mat (With Backlash, with a speed loop on the impression roll .. no l/l in the speed feedback of the blanket roll, impression roll or chill roll)

Figure 3-1. Registration error (w/spd, w/BL)

Figure 3-2. Position error (w/spd, w/BL)

Figure 3-3. Tensions (w/spd, w/BL)

Figure 3-4. Torques (w/spd, w/BL)

Figure 3-5. Surface speeds (w/spd, w/BL)

Set (2):

Plots for test15.mat (No Backlash, with a speed loop on the impression roll .. no l/l in the speed feedback of the blanket roll, impression roll or chill roll)

Figure 3-6. Registration error (w/spd, wo/BL)

Figure 3-7. Position error (w/spd, wo/BL)

Figure 3-8. Tensions (w/spd, wo/BL)

Figure 3-9. Torques (w/spd, wo/BL)

Figure 3-10. Surface speeds (w/spd, wo/BL)

Set (3):

Plots for test2.mat (With Backlash, without a speed loop on the impression roll .. no l/l in the speed feedback of the blanket roll, impression roll or chill roll)

Figure 3-11. Registration error (wo/spd, w/BL)

Figure 3-12. Position error (wo/spd, w/BL)

Figure 3-13. Tensions (wo/spd, w/BL)

Figure 3-14. Torques (wo/spd, w/BL)

Figure 3-15. Surface speeds (wo/spd, w/BL)

Set (4):

Plots for test7.mat (No Backlash, without a speed loop on the impression roll .. no l/l in the speed feedback of the blanket roll, impression roll or chill roll)

Figure 3-16. Registration error (wo/spd, wo/BL)

Figure 3-17. Position error (wo/spd, wo/BL)

Figure 3-18. Tensions (wo/spd, wo/BL)

Figure 3-19. Torques (wo/spd, wo/BL)

Figure 3-20. Surface speeds (wo/spd, wo/BL)

Set (5):

Plots for test3.mat (With Backlash without a speed loop on the impression roll .. with l/l in the speed feedback of the blanket roll, none in the speed feedback of the impression roll or chill roll)

Figure 3-21. Registration error (wo/spd, w/BL, L/L in BR)

Figure 3-22. Position error (wo/spd, w/BL, L/L in BR)

Figure 3-23. Tensions (wo/spd, w/BL, L/L in BR)

Figure 3-24. Torques (wo/spd, w/BL, L/L in BR)

Figure 3-25. Surface speeds (wo/spd, w/BL, L/L in BR)

Set (6):

Plots for test4.mat (No Backlash without a speed loop on the impression roll .. with l/l in the speed feedback of the blanket roll, none in the speed feedback of the impression roll or chill roll)

Figure 3-26. Registration error (wo/spd, wo/BL, L/L in BR)

Figure 3-27. Position error (wo/spd, wo/BL, L/L in BR)

Figure 3-28. Tensions (wo/spd, wo/BL, L/L in BR)

Figure 3-29. Torques (wo/spd, wo/BL, L/L in BR)

Figure 3-30. Surface speeds (wo/spd, wo/BL, L/L in BR)

Set (7):

Plots for test5.mat (With backlash, with a speed loop on the impression roll .. with l/l in the speed feedback of the blanket roll and the impression roll, none in the speed feedback of the chill roll)

Figure 3-31. Registration error (w/spd, w/BL, L/L in BR, CR)

Figure 3-32. Position error (w/spd, w/BL, L/L in BR, CR)

Figure 3-33. Tensions (w/spd, w/BL, L/L in BR, CR)

Figure 3-34. Torques (w/spd, w/BL, L/L in BR, CR)

Figure 3-35. Surface speeds (w/spd, w/BL, L/L in BR, CR)

Set (8):

Plots for test9.mat (No Backlash, with a speed loop on the impression roll .. with l/l in the speed feedback of the blanket roll and the impression roll, none in the speed feedback of the chill roll)

Figure 3-36. Registration error (w/spd, wo/BL, L/L in BR, CR)

Figure 3-37. Position error (w/spd, wo/BL, L/L in BR, CR

Figure 3-38. Tensions (w/spd, wo/BL, L/L in BR, CR

Figure 3-39. Torques (w/spd, wo/BL, L/L in BR, CR

Figure 3-40. Surface speeds (w/spd, wo/BL, L/L in BR, CR

Set (9):

Plots for test8.mat (With Backlash, with a speed loop on the impression roll .. with l/l in the speed feedback of the blanket roll, impression roll and chill roll)

Figure 3-41. Registration error (w/spd, w/BL, L/L in BR, IR, CR)

Figure 3-42. Position error (w/spd, w/BL, L/L in BR, IR, CR)

Figure 3-43. Tensions (w/spd, w/BL, L/L in BR, IR, CR)

Figure 3-44. Torques (w/spd, w/BL, L/L in BR, IR, CR)

Figure 3-45. Surface speeds (w/spd, w/BL, L/L in BR, IR, CR)

Set (10):

Plots for test10.mat (No Backlash, with a speed loop on the impression roll .. with l/l in the speed feedback of the blanket roll, impression roll and chill roll)

Figure 3-46. Registration error (w/spd, wo/BL, L/L in BR, IR, CR)

Figure 3-47. Position error (w/spd, wo/BL, L/L in BR, IR, CR)

Figure 3-48. Tensions (w/spd, wo/BL, L/L in BR, IR, CR)

Figure 3-49. Torques (w/spd, wo/BL, L/L in BR, IR, CR)

Figure 3-50. Surface speeds (w/spd, wo/BL, L/L in BR, IR, CR)

Set (11):

Plots for test11.mat (Backlash, without a speed loop on the impression roll .. with l/l in the speed feedback of the Blanket roll and Chill roll, none in the speed feedback of the Impression roll)

Figure 3-51. Registration error (wo/spd, w/BL, L/L in BR, CR)

Figure 3-52. Position error (wo/spd, w/BL, L/L in BR, CR)

Figure 3-53. Tensions (wo/spd, w/BL, L/L in BR, CR)

Figure 3-54. Torques (wo/spd, w/BL, L/L in BR, CR)

Figure 3-55. Surface speeds (wo/spd, w/BL, L/L in BR, CR)

Set (12):

Plots for test12.mat (No Backlash, without a speed loop on the impression roll .. with l/l in the speed feedback of the Blanket roll and Chill roll, none in the speed feedback of the Impression roll)

Figure 3-56. Registration error (wo/spd, wo/BL, L/L in BR, CR)

Figure 3-57. Position error (wo/spd, wo/BL, L/L in BR, CR)

Figure 3-58. Tensions (wo/spd, wo/BL, L/L in BR, CR)

Figure 3-59. Torques (wo/spd, wo/BL, L/L in BR, CR)

Figure 3-60. Surface speeds (wo/spd, wo/BL, L/L in BR, CR)

Set (13):

Plots for test13.mat (With Backlash, without a speed loop on the impression roll .. with no l/l in feedback of blanket roll and impression roll, l/l in feedback of chill roll)

Figure 3-61. Registration error (wo/spd, w/BL, L/L in CR)

Figure 3-62. Position error (wo/spd, w/BL, L/L in CR)

Figure 3-63. Tensions (wo/spd, w/BL, L/L in CR)

Figure 3-64. Torques (wo/spd, w/BL, L/L in CR)

Figure 3-65. Surface speeds (wo/spd, w/BL, L/L in CR)

Set (14):

Plots for test14.mat (No Backlash, without a speed loop on the impression roll .. with no l/l in feedback of blanket roll and impression roll, l/l in feedback of chill roll)

Figure 3-66. Registration error (wo/spd, wo/BL, L/L in CR)

Figure 3-67. Position error (wo/spd, wo/BL, L/L in CR)

Figure 3-68. Tensions (wo/spd, wo/BL, L/L in CR)

Figure 3-69. Torques (wo/spd, wo/BL, L/L in CR)

Figure 3-70. Surface speeds (wo/spd, wo/BL, L/L in CR)

CHAPTER 4

OBSERVATIONS AND RECOMMENDATIONS

Observations

The plots of all the sets shown in Chapter 3, indicate that little relative improvement was made when any of the typical control approaches to compensating for gear-backlash were implemented. It is the author’s opinion, that the main reason for the ineffectiveness of these control schemes is due to the surface speed jitter in the impression roll.

Given that the impression roll inertia, and the reflected inertia of the impression roll motor at the strip are of the same order of magnitude, and relatively low, the motor speed regulator will not have any trouble tracking a speed reference, even in the presence of gear-backlash. This is so, despite any large changes that may occur in the surface speed of the impression roll. Evidence of this was obtained in the simulation results (not presented), which showed that the motor speed was significantly less noisy than the surface speed of the impression roll.

On the blanket roll however, the reflected motor inertia, at the blanket roll surface, was an order of magnitude smaller than the blanket roll. This indicates that backlash will be a significant problem in terms of tuning the speed regulator for tracking a speed reference, however, a hidden benefit is that the surface speed of the blanket roll will not deviate as much as the impression roll, given the same magnitude of a given load disturbance. In fact the blanket roll gears should stay fairly well loaded on one side of the gear surface. The same cannot be said for the impression roll. It is likely that the impression roll is bouncing in and out of a loaded gear condition, as each impression is made, and as any load disturbances from the process are injected into the coupled system.

It is also highly likely that the exit chill roll of the printing section (and in all likelihood the entire chill section) introduce some web surface speed deviations into the impression roll section of the coater through the coupled web material. These disturbances will tend to cause the impression roll to break in and out of an oscillatory unstable condition, while at the same time the blanket roll may remain fairly well behaved. This phenomena is exaggerated by the fact that the blanket roll surface is loosely coupled to the web through an impression and a thin layer of coating material, while the impression roll is tightly coupled to the web, through a set tension, and a large wrap angle.

Several drive regulator configuration options could help this alleviate the sensitivity of the impression roll to backlash, but these would only assist in making the drive speed feedback look better, they will not in any way help with the effect of a attenuating deviations in the impression roll surface speed as long as there is backlash in the impression roll gear-train.

To summarize the observations made from the simulations:

The existence of backlash in this mechanical configuration is extremely depilatory to the accuracy of the coating registration.
The system is most sensitive to the existence of backlash in the drive train of the impression roll.
Small improvements in system registration can be made with modifications to the existing control scheme.
Existence of tension deviations in the chill section of the printing section will cause problems in the registration of the coating section.

Recommendations

The following recommendations are based on observations made during the simulation, and discussions with several systems engineers at the drive vendor:

If the coupling between the printing process chill section and the impression roll is tight, and the exit speed of the mechanical line shafted printing section is stiff, the use of a speed regulator on the impression roll will lead to the interactions that were described earlier, and cause the impression roll surface speed to bounce around. To alleviate the possibility for this type of interaction, we recommend configuring the impression roll as a torque regulator, or at the least, a soft speed regulator with a significant amount of current compounding.
The simulations show clearly that the existence of backlash in all the drive trains severely impacts the registration between the blanket roll and the impression roll. To alleviate this as a possible source of contention between the desire to regulate good surface speed, and compensate for gear backlash, the mechanical configuration should be looked at, with the aim in mind of removing backlash from the drive-trains. This is especially true for the impression roll drive-train.
Given that the above actions result in a substantial improvement in the consistency of registration, the registration loop should be enabled and tuned.

This concludes the engineering report.

BIBLIOGRAPHY

[1] Boulter, B.T. Fox, H.W.,"Advanced Dynamic Simulation", Internal ApICS Systems Engineering Training Course.

[2] Carter, W.C., "Reducing Transient Strains in Elastic Processes" , Control Engineering Mar. 1965. pp. 84-87.

[3] Hess, D.P., Soom, A. "Friction at a Lubricated Line Contact Operating at Oscillating Sliding Velocities" Journal of Tribology Transactions of the A.S.M.E. Vol 112, pp 147-152, 1992.

[4] Majd, V.J.. Simaan M. A., "A Continuous Friction Model For Servo Systems With Stiction", Proceedings of the 4^th I.E.E.E. Conference on Control Applications, Albany NY. 1996.

[5] Boulter, B.T., "The Effect of Speed-loop Bandwidths and Line Speed on System Eigenvalues in Multi-Span Web Transport Systems", Transactions of the I.E.E.E. I.A.S Society, June/July 1998.