Theoretical Investigation on Performance Characteristics of Aerostatic Journal Bearings with Active Displacement Compensator

Round 1

Reviewer 1 Report

The article studies the performance characteristics of aerostatic journal bearing with active displacement compensator. A counter-matrix sweep method has been developed for solving linear and nonlinear boundary value problems in partial derivatives with respect to the function of the square of the pressure in the bearing gap and inter throttling bearing cavities for any values of the relative shaft eccentricity. According to the theoretical and experimental results, bearings with a throttle system have the best quantitative and qualitative load characteristics.
The novel findings in the paper can be helpful for design and analysis of journal bearings. However, some issues should be addressed that can contribute for an improvement of the quality.
1. For the stationary Reynolds equation, the initial oil film thickness is expressed by Eq. (2), but why the right hand side of eq.(1) equals to zero?
2. More in depth literature review is needed. A lot of old references are cited. Many people are working in recent time to improve the performance of journal bearings. See, Mechanical Systems and Signal Processing,150,2021,107227.  
3. What do you think about cavitation modes? Could these support the results and in which way?
4. Please show the Hersey and the Reynolds numbers, indicated in the results section, the lubrication regime that the bearing operates.
5. The parameters' influence on the bearing performance, such as the aspect ratio of the bearing, the temperature and load effects on the aero viscosity are not investigated.
6. For the aero bearings, the flow of fluid is turbulent. Please clarify your reason for choosing the laminar fluid model.

Author Response

1. The right side of equation (1) is equal to zero because the model does not take into account the shaft rotation speed.
2. The literature review has been fundamentally revised.
3. There is no cavitation in gas-lubricated bearings.
4. The model contains the following assumptions: the ratio of the transversal and longitudinal linear scales, as well as the ratio of the air velocity scales in the lubricating layer is much less than one, so the flow inertia can be neglected; the temperature in the lubricating layer is constant, hence the constancy of the air viscosity coefficient. Hersey's number was neglected because rotational speed was not taken into account. When air moves in the lubricating layer, the thickness of the gap is small; therefore, the movement of the lubricant can be considered laminar. Turbulence occurs only at very high shaft rotation speeds and high inlet pressures, but, as mentioned above, the speed was not taken into account in the model. Therefore, the Reynolds number for air flow in aerostatic bearings is very small.
5. The specified parameters have an impact on the bearing characteristics, however, the main attention was paid to the study of the influence of those parameters that have the main influence on the static and dynamic characteristics of the bearing - the throttling system adjustment factors, the number of gas film squeezing, the inter-throttle chamber volume, and the elastic suspension compliance.
6. The answer to this question is set out in paragraph 4.

Reviewer 2 Report

The paper is well done (even if the many formulas in my opinion divert attention from the physical description of the system), perhaps the authors could give some more information on the experimental part.

Note: on p. 23 lines 692-695 repeat lines 688-691

Author Response

Unfortunately, it is impossible to give comparative data on gas bearings with an external combined throttle system and an elastic displacement compensator, since, according to our information, such studies have not been carried out.

The indicated error has been fixed.

Reviewer 3 Report

The paper discusses the modelling of an aerostatic radial bearing with an external combined throttling system and an elastic displacement compensator. Such bearings are an alternative to gas bearings with air flow compensators. The authors showed the advantages of the analysed bearings using the computational method. The various characteristics of an aerostatic radial bearing are presented and discussed in this paper.

The subject of the paper is very interesting and important at the moment. The manuscript is carefully prepared and overall I rate it very well. Before publishing in the journal, I suggest that authors consider improving a few elements.

1. The list of literature includes many publications from the 1960s, 1970s and 1980s. There are only a few publications from recent years. Therefore, I encourage authors to update the literature review and include more recent publications.
2. The experimental verification of the model is very superficial and based on the publications of other authors. The cited publication concerns aerostatic gas bearings, not bearing with an external combined throttling system and an elastic displacement compensator. Authors should better justify this approach or extend the scope of verification.

Author Response

1. The list of references has been radically revised and updated.
2. The authors agree with the reviewer regarding the experiment, however, they believe that the data presented generally confirm the theoretical results obtained - they give a satisfactory agreement between the static characteristics and indicate a qualitative agreement between the dynamic indicators.
3. Unfortunately, it is impossible to give comparative data on gas bearings with an external combined throttle system and an elastic displacement compensator, since, according to our information, such studies have not been carried out.

Round 2

Reviewer 1 Report

I recommend publication.