Analysis and Suppression of Self-Excited Oscillations in Pressure Servo Valve System

Round 1

Reviewer 1 Report

The paper title clearly describes the content of the work. The paper is well written and the quality of the figures is acceptable. The paper is interesting with some valuable conclusions and is recommended for possible publication in Applied Sciences (ISSN 2076-3417) journal.

Authors have conducted an experimental and analytical investigation on the suppression of self-excited oscillations in pressure servo valve systems. 

1. Please discuss how the findings in this work relate to existing studies in this area.

2. What are the limitations of this study? 

3. The authors should present the key contribution of this manuscript clearly and illustrate the importance of this study. 

4. In the used test rig, the measuring devices used in the experiment should be described clearly with inserting the accuracy of each one. For example, what is the type of the used pressure gauge and its accuracy?

Author Response

First of all, thank you for reviewing our article and giving a high evaluation. In response to your review comments, we made the following reply.

• The research results of this paper are based on the mature nonlinear system vibration theory. Compared with the research in the same field, the main difference of this paper lies in the different research objects. Aiming at the pressure oscillation of the PSVS in practice, this paper analyzes the vibration mechanism, and defines the vibration as self-excited oscillation caused by the unreasonable structure of the pressure servo valve. On this basis, the targeted oscillation suppression methods are studied, and the effective vibration suppression is preliminarily realized.
• The limitation of this paper is that the vibration mechanism and vibration suppression method are only applicable to the special research object of PSVS. However, the analysis method in this paper can be extended to similar dynamic systems.
• The main contribution of this paper and the importance of research are supplemented in the conclusion of the revised manuscript. This paper comes from the real vibration problem in the brake pressure control system of a large aircraft. The research results explain the causes of vibration in the system. At the same time, this paper also provides an effective technical means for the vibration suppression of such system.
• In this paper, the pressure sensor is used to monitor the output pressure and the backpressure of PSVS. The pressure sensor is introduced in the second section of this paper (Figure 7).
• The author makes a supplementary explanation for each formula in the modeling process, so that reviewers can understand the principle and logic of the model. The simplified model in this paper is based on the original model to a certain extent. There are mainly two simplified contents: First, the load flow of the main valve spool of the pressure servo valve is simplified from the complex nonlinear form of sign function in formula (8) to the linear form shown in formula (32). It should be noted that this linearization method is recognized in engineering applications; Secondly, the backpressure is simplified from the complicated time-varying calculation method in subsection 2.2 to a fixed value(p_h=0.6MPa). This is because after the structure optimization, the backpressure of the PSVS can be approximately considered as a constant value. This part is introduced in detail in subsection 4.1 of the paper.

Author Response File: Author Response.docx

Reviewer 2 Report

The manuscripts aim to discuss the self-excited oscillations in a valve system. The authors provide some equations and figures for illustrating the system’s behaviours. Many details are missing, and the text looks like a draft report of the performed actions. Therefore, I can not recommend the manuscript for publishing.

There are several manor issues with the manuscripts.

There is no proper introduction to the topic. The novelty is not stated. For example, a similar effect was discussed in the following papers: Nonlinear Dyn (2021) Vol. 103, pages 2315–2327 and Journal of Mechanical Science (1968) Vol 10, Number 4, pages 306-318. The later paper is quite old, and the former is very recent. What did happen during this time span? The current review is not focused on the valve system and does not reflect the progress in the area. The phrase “many scholars in this field have devoted a great deal of energy to carry 34 out the following related research work” is not good enough to introduce the problem.

 

The model’s description is effectively missing. I was not able to understand the principle and logic of the model. The authors refer to Ref. [14], which is not available. There is no discussion of the model’s relevance to the previous research. Also, there is no explanation of which parameter controls the self-oscillations. The Andronov-Hopf bifurcation was not demonstrated. The emphasis on the step and ramp signals is misleading. There is no formal analysis of equilibrium states.

 

The last sections are too brief for understanding. Since the authors do not analyse the initial model, the analysis of reduced models in sections 3 and 4 is hardly understandable. First, the authors claim that additional forced oscillations can suppress the oscillations, then consider standard feedback loop analysis. As a result, the text is a mess.

Author Response

First of all, thank you for reviewing our paper. At the same time, we are sorry that our paper has caused you confusion. In response to your review comments, we made the following reply.

• The introduction of this paper has been greatly adjusted, focusing on the research status of self-excited oscillation of hydraulic valves and valve-controlled systems. It is found that there is little research on the self-excited oscillation mechanism and suppression method of special pressure servo valve system, and the research in this paper is original.
• The author makes a supplementary explanation for each formula in the modeling process, so that reviewers can understand the principle and logic of the model. The simplified model in this paper is based on the original model to a certain extent. There are mainly two simplified contents: First, the load flow of the main valve spool of the pressure servo valve is simplified from the complex nonlinear form of sign function in formula (8) to the linear form shown in formula (32). It should be noted that this linearization method is recognized in engineering applications; Secondly, the backpressure is simplified from the complicated time-varying calculation method in subsection 2.2 to a fixed value(p_h=0.6MPa). This is because after the structure optimization, the backpressure of the PSVS can be approximately considered as a constant value. This part is introduced in detail in subsection 4.1 of the paper.
• In this paper, the influencing factors of self-excited oscillation of pressure servo valve system are qualitatively analyzed in section 4.1. However, since this paper starts with the phenomenon of pressure oscillation, it aims to clarify the inducement of its self-excited oscillation and take targeted oscillation suppression measures. Therefore, the theory of nonlinear system such as Andronov-Hopf bifurcation is not involved. Whether the dynamic behavior of self-excited oscillation of PSVS will appear Andronov-Hopf bifurcation or tend to chaos remains to be further studied. In the research, this paper mainly analyzes the PSVS under the step and ramp signals, because the self-excited oscillation phenomenon analyzed in this paper comes from the brake pressure servo control system of a large aircraft, and the control signal used by such a system in normal operation is the step or ramp signal. In order to ensure the good consistency between the research results of this paper and the actual engineering situation, the author used these two input signals in the analysis.
• In subsection 2.3.2 of the paper, the author analyzed the output pressure of the stable oscillation section, and uses the FFT method to analyze the frequency domain characteristics of the oscillation.
• The reference [12] in this paper is the doctoral dissertation of the corresponding author, which can be searched in CNKI. Because this dissertation is written in Chinese, it may be difficult to search in the English scientific papers database.
• This paper does not claim that additional forced oscillation can suppress the self-excited oscillation of the pressure servo valve system. In section 4.1, it is proved that the self-excited oscillation of the system is caused by the positive feedback of backpressure. Therefore, it can be inferred that if the backpressure is not a fluctuating time variable but a fixed value, the positive feedback effect can be eliminated, that is, the self-excited oscillation of the system can be suppressed. Furthermore, through simulation analysis, it is found that the backpressure can be approximately regarded as a fixed value after the damping hole is added and the open cavity structure is adopted. Therefore, in this paper, the self-excited oscillation of the system is effectively suppressed by eliminating the fluctuation of backpressure.

 

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

I thank the authors for their efforts to improve the manuscript. The response notes and the revised manuscript made the latter more understandable. However, the core of my initial concern remains untouched. Therefore, I can not recommend the manuscript for publishing.

 

The manuscript lacks logic. The authors introduce the block diagram with the feedback loops in section 4.2. Why can the same approach be used from the beginning? Note that the conducted analysis is questionable since the authors did not specify the equilibrium state (initial conditions). The Laplace transform is incorrect without them. The authors ignored and did not address my previous comment: there is no formal analysis of equilibrium states. Why do the authors need a model if it is not utilised? Moreover, the way the model’s presentation does not allow a reader to verify the correctness of the model’s implementation in the Simulink. The parameters’ values and details of the numerical scheme are missing.

 

The emphasis on the step and ramp signals is misleading. Experimental measurements in Fig.9(a) show that the oscillations appear for particular values of the pressure (see time around 4). The presented analysis is very weak. A different amplitude of the step input could be considered, or an adiabatic increase of the pressure could be realised. Currently, the presented results do not confirm the claims.

 

Why do the authors ignore the provided references? I still believe that there is no proper introduction to the topic. The model should be compared to similar ones which are available in the literature.

 

Also, English requires additional attention. The current text is hardly understandable.

 

I do not see how incremental improvements in the manuscript could change my opinion. The authors should write a new manuscript or perform an additional investigation.

 

Author Response

Thank you for reviewing our article. In response to your review comments, we made the following reply.

• The reviewer thinks that this article lacks logic, but does not explain it in detail. Therefore, I cannot agree with this point. In this article, the oscillation mechanism of aircraft brake pressure control system is analyzed, and the oscillation suppression method is proposed, and the stability margin analysis is carried out in order to ensure that the new system has sufficient stability margin. At last, the analysis results show that the proposed vibration suppression method is effective.At the same time, the opinions put forward by the reviewers (The authors introduce the block diagram with the feedback loops in section 4.2. Why can the same approach be used from the beginning?) are not logical, and it is difficult for me to understand what the reviewers want to express.
• The author has explained the equilibrium state in the first reply to the reviewer's question. In this article, the initial condition of Laplace transformation is the equilibrium state (input current is 40mA, and output pressure is about 9.5MPa which is shown in Figure16).
• I can't understand the reviewers' opinions “Why do the authors need a model if it is not utilized?” In this article, the model of PSVS is used in the time-domain analysis, frequency-domain analysis and stability margin analysis. What does the reviewer mean by saying that the model is not utilized?
• In order to make the Simulink model more regular, the pressure difference and back pressure are modularized by author. The models used in the pressure difference module and back pressure module are introduced in Section 2.2 of this article, which is easy to understand if the reviewer has the basic knowledge of hydraulic system.

The pressure difference module is

The back pressure module is

• In the first reply to the reviewer, the author explained that the input signal was consistent with the actual aircraft wheel brake system.。The original intention of this article is to solve the system oscillation problem under specific demand conditions. If the input conditions are not consistent with the actual situation, the analysis results are meaningless.
• The reviewer mentioned two references, but did not give the name and author of the article, so I can't find it. At the same time, the author believes that any nonlinear system is unique, and its composition and response under specific conditions are unique too. In this case, the modeling methods in those two references and the model in this article do not necessarily have the significance of comparison. In the revised introduction of this article, the research status of self-excited oscillation of hydraulic valve and valve control system is discussed. The author thinks that its content is directly related to this article and can support the research content of this article.

Author Response File: Author Response.docx