Developing Digital Observer of Angular Gaps in Rolling Stand Mechatronic System

Round 1

Reviewer 1 Report

The paper considers developing an observer of angular gaps in the spindle joints of the ‘electric drive-stand’ mechatronic system of the plate Mill 5000 of Magnitogorsk Iron and Steel Works PJSC (MMK PJSC). This is an interesting work. But it requires clarifying some questions before it can be published.   Main comments:

1. About the working conditions, is this result only for the current spindle speed, working load, and roll radius? Can it be used for the various working conditions of the same plate Mill 5000?
2. Equations (1) and (2) are based on the assumption that the speed changes linearly at curve 1. How much is the error of equations (1) and (2) if the linearity is not followed?
3. The authors compared amplitudes in figure 8 and figure 5 and confirm that the actual gap is about 2 degrees. I don't agree that the value "2 degrees" is the actual gap value because Figure 8 is obtained from the Matlab Simulink simulation, not from real measurement. Did the authors measure the gap actually to verify the gap value?
4. As mentioned in line 441, building empirical dependences of the spindle joint wear on the angular gap. The angular gap may be affected by many reasons, for example, the spindle joint wear, the roll wear, and so on. How to clarify the main cause of the angular gap is the spindle joint wear?
5. The authors did provide a procedure to calculate the gap by indirect method. But they did not provide the accuracy of the model from the real data.

    Minor comments:

1. Why does it have a 1/2 coefficient in equation (1)?

Author Response

Dear Reviewer,

Thank you for your review of our paper and comments that will improve its quality.

Below are the answers to your comments:

1. About the working conditions, is this result only for the current spindle speed, working load, and roll radius? Can it be used for the various working conditions of the same plate Mill 5000?

To answer the questions, the following paragraph has been added to Section «5. Conclusions».

The paper provides the experimental results for specific spindle speeds, workloads, and roll radii. These conditions have not been chosen specially and are typical for the Mill 5000. Similar results have been obtained when rolling various types of sheets. The rolling conditions do not affect the spindle joint gap, which is determined by the wear of the spindle joint elements and the roll blades. Therefore, the results obtained are reliable. This is confirmed by the results of long-term pilot tests of the algorithm implemented.

2. Equations (1) and (2) are based on the assumption that the speed changes linearly at curve 1. How much is the error of equations (1) and (2) if the linearity is not followed?

To answer the question, the following paragraph has been added.

The linear change in speed is ensured with virtually no error when it is set so (curve 1) in drives with PI speed controllers. This is because in closed doubly integrating systems, the dynamic error of the command-based parameter control is zero. Therefore, the error in the angular gap calculation according to equation (1) will also tend to zero. For the cases with non-linear changes in speed, the product of the speed and time increments should be replaced by the speed integral over time. This is noted in the algorithm description.

3. The authors compared amplitudes in figure 8 and figure 5 and confirm that the actual gap is about 2 degrees. I don't agree that the value "2 degrees" is the actual gap value because Figure 8 is obtained from the Matlab Simulink simulation, not from real measurement. Did the authors measure the gap actually to verify the gap value?

The authors agree with the comment. The phrase that the actual gap value is 2 degrees has been removed.

4. As mentioned in line 441, building empirical dependences of the spindle joint wear on the angular gap. The angular gap may be affected by many reasons, for example, the spindle joint wear, the roll wear, and so on. How to clarify the main cause of the angular gap is the spindle joint wear?

Spindle joints are mating parts ensuring the articulation of two rotating assemblies - the spindle and the roll. for the articulation of two rotating devices - directly the spindle and the roll. This is specified in lines 168-171 of the original text.

In reply to the comment, the following paragraph has been added.

The roll diameter and wear and other external factors cannot affect the internal gap between the rectangular roll blade and the joint elements shown in Fig. 3b. The main (and only) reason for increasing angular gaps is the wear of the spindle joint elements and the roll blade. Therefore, the gap value is a diagnostic feature unambiguously and reliably characterizes the joint wear degree.

5. The authors did provide a procedure to calculate the gap by indirect method. But they did not provide the accuracy of the model from the real data.

In reply to the comment, the following paragraph has been added.

The model adequacy to the object under study is not checked here since it has a known structure, and the simulated object parameters have been taken from the afore-mentioned paper [43]. The paper considers the simulation of transients during the biting with open and closed gaps in spindle joints. Comparing calculations with experimental oscillograms has proven their coincidence with satisfactory accuracy. Therefore, re-checking the adequacy is not required.

and

1. Why does it have a 1/2 coefficient in equation (1)?

The equation has the factor ½ since the angular gap is calculated as the area of the triangle bounded by curves 2 and 3 (considering the [rpm] to [rad/s] conversion factor). The right triangle area is ½ the product of its legs (in our case, these are Δn and Δt).

Reviewer 2 Report

This paper deals with an observer-based approach for fault detection in rolling mill’s main drive with independent roll drives. The method is based on the design of a mechanical transmission angular gap observer.

The physical model of the system is presented in the diagram of figure 2. This diagram shows a relatively linear model for a complex system whose dynamic is nonlinear, and if one considers the backlash existing in the gears of transmission the system becomes discontinuous.

1) What is the influence of the difference between the real dynamics of the system and the considered model on the convergence of the observer?

Although I am not an expert in the theory of observers, I know that the theoretical power of an observer comes from the proof of its stability (of its convergence). For nonlinear systems, Lyapunov's theory is the most used.

2) In this paper, no stability analysis is performed, why? even if the experimental results confirm the effectiveness of the method, it is in my opinion necessary to formally demonstrate the stability of the observer.

Author Response

Dear Reviewer,

Thank you for your review of our paper and comments that will improve its quality.

Below are the answers to your comments:

1. What is the influence of the difference between the real dynamics of the system and the considered model on the convergence of the observer?

The only non-linearity affecting the parameter restoration (calculation) accuracy is the angular gap. Block 5 in the structure in Fig. 2 represents this non-linearity. The model adequacy to the object under study - the Mill 5000 drive has been proven in a previously published paper [43]. Therefore, in our opinion, additionally estimating the convergence of the results is not required.

Although I am not an expert in the theory of observers, I know that the theoretical power of an observer comes from the proof of its stability (of its convergence). For nonlinear systems, Lyapunov's theory is the most used.

Lyapunov's theory is used to test the stability of closed automated control systems. Information-and-measuring systems with observers do not require checking the stability. Therefore, a comparison of the calculated and experimental results is quite sufficient.

2. In this paper, no stability analysis is performed, why? even if the experimental results confirm the effectiveness of the method, it is in my opinion necessary to formally demonstrate the stability of the observer.

In reply to the comment, the following paragraph has been added.

The observer scheme shown in Fig. 6 is an open-circuited structure. It is an element of a diagnostic system not affecting the processes occurring in the electromechanical system studied. Therefore, checking the observer stability (convergence) is not required.

Round 2

Reviewer 1 Report

I think the authors have revised the manuscript carefully. I recommend accepting for publication.