Analysis of Hydrostatic Bearings Based on a Unstructured Meshing Scheme and Turbulence Model

Round 1

Reviewer 1 Report

Suggestions for Literature Survey:

1.     Instead of using full name (Shao JP et al.) of authors in Line 39, it is usually the family name (Shao et al.) used in citation. Please modify the same problems in Line 42, 47, 52, 54, 60, 63, 66, 72, 74, 77, 79, 96 of the introduction section.

2.     Please add more the latest literature review from the year 2020 to 2022 in the fields of FEM/Fluent/CFD grid modeling or mesh modeling of hydrostatic bearings.

 

Some problems of terminology frequently used in hydrostatic bearing:

3.     It is better to replace the term “supporting capacity” by the term of “supporting load capacity” in Line 108, 116, 117, 122, 164, 173, 203, 212, 216, 233, 240, 245, 246, 251, 252, 259, 260, 262, 275, 323.

4.     It is also better to replace the term “supporting capacity” by the term of “supporting load capacity” in Figure 7 and Figure 9.

5.     In order to unify the same terminology, it is better to replace the term “bearing force” by the term of “bearing load capacity” in Figure 10.

6.     In Figure 2, three terminologies would be better to change to correct ones.  It is better to replace the term “guideway” by “fixed guide rail”. “Sealing surface” would be better to change to “Bearing land surface”. “Oil chamber” would be better to change to “Oil recess”.

7.     It would be better to use the term “Bearing land width”, instead of “Seal band width” in Line 123 and in Table 1.

8.     In Figure 3, “Oil sealing surface” would be better replaced by “Bearing land surface”.

9.     Between Line 127 and Line 128, “fluidic resistor of seal band” would be better replaced by “flow resistance of bearing land”.

10.  It would be better to use the term “time-variant”, instead of “time-varying” in Line 259.

 

Some mistakes in the text:

11.  There is a mistake in Line 132, μ is “dynamic viscosity”, instead of “density”.

12.  In Table 1 and Table 2, the initial film thicknesses are different.  The initial film thickness is 0.025mm (25μm) in Table 1, but the initial film thickness is 30.1 μm in Table 2.  Which one is the correct initial film thickness for this study?

13.  In Line 263, the film thickness is 20 μm.  Why do the authors calculate the average damping in 20 μm, instead of 25μm or 30.1 μm?  Please explain the reasons why you try three different film thickness in analyses?

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The work carried out modeling and research of static and dynamic characteristics of a hydrostatic guide with the function of supporting and moving heavy parts, taking into account the cutting forces that are processed on ultra-precise and heavy-duty machines. With the article, simplified formulas for calculating the load and stiffness are proposed, as well as the calculation of the dynamic criteria of the guide based on the innovation of the general structure of the three-dimensional grid of the global model of the flowing liquid region. The article provides a fairly complete literature material, an analysis of the state of the problem, on the basis of which a conclusion is made about the relevance of this study.

The study presented in the article has some shortcomings, and the reviewer has comments, which are presented below.

1. In our opinion, the simplified formula (1) used to calculate the bearing capacity does not take into account the areas of squares that are located along the four edges of a thin gap of thickness h. A more accurate formula for the effective bearing surface area is Ae = LB-Lb-Bl+2bl. Accounting for the specified area allows you to increase the accuracy of the calculation of the bearing capacity by 3%. Similarly, in formula (2) for the flow resistance in a thin lubricating layer, this remark must also be taken into account, since the outflow will occur over a slightly increased area, which will lead to an increase in fluid flow rate.

2. It is impossible to understand from what considerations formula (3) was obtained. Probably, it was obtained on the basis of the formula for the equality of lubricant flow rate through the input throttle and the carrier gap. But there is no such formula in the article. Since Figure 2 does not give an idea of what kind of throttle is used (nozzle, capillary, something else), it is impossible to assess how true formula (3) is. It is also not clear what the coefficient alpha = 0.6 is and there is no source to make it fashionable to understand on what basis it is applied. In passing, we note that the text of section 2.1 should be edited, it lacks a comma after formulas (3), (4), instead of a dot, there should also be a comma before the word “where”. The variable K before formula (4) must be in italics. There are errors with subscripts of values.

3. Even more questions are raised by formula (7), which is used to evaluate damping. As you know, damping is a dynamic quantity, its formula can be obtained on the basis of an analytical solution of a boundary value problem for the Reynolds differential equation. Here we don't see it. Most likely, formula (7) shows the flow rate associated with the extrusion of liquid in the gap. But then the value of the rate of change of the gap h should be present in the formula, which we do not see in this formula. Here it is necessary to give explanations and a link to the source.

4. The authors write “The oil is governed by a modified N-S equation. In the Reynolds average method…”, however, what is meant by this equation and what “Reynolds average method” is in question is completely incomprehensible, because there are no references to primary sources. It also requires rigorous justification of the method underlying the model for subsequent calculations. The same applies to equations (11) - (13).

5. The authors write that the hydrostatic guideway bearing needs to have the high supporting capacity and stiffness…or this reason, the recommended oil film thickness between the bearing and the guideway is only 20 μm.” However, it is known that the bearing capacity of a hydrostatic bearing does not depend on the thickness of the gap, it depends only on the area of the bearing surfaces and the pressure in the chamber. Stiffness really depends on the clearance. Thus, this part of the article should be edited.

6. The authors use the bearing stiffness criterion. This criterion is used by many researchers, without thinking that from the point of view of the methodology for modeling the dynamics of machines and their statics, as a special case of dynamics, this term is unsuccessful. It contradicts the main provisions of the theory of automatic regulation and control of dynamic objects. According to this theory, the study of the dynamics of objects is based on the use of the so-called transfer functions, which are the ratio of output values to input values. With regard to machine tool bearings, the input value is the load on the bearing, and the output values are gap, pressure in chamber, lubricant flowrate and bearing capacity. Thus, the correct value is "compliance" -dh/df, i.e. the ratio of the output clearance value to the input load value, but not vice versa -df/dh, which is the stiffness. This paragraph is not a criticism of the theory presented by the authors. This is a note for reflection in order to more carefully select the correct criteria for the operation of bearings.

In general, the article can be recommended for publication after correcting the shortcomings, taking into account the comments made.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Review of the paper entitled “Characteristics analysis and optimization of hydrostatic bearing

via multi-scale global fluid domain accurate model”.

 

This  work studies a hydrostatic bearing and proposes a vortex suppression method. I cannot judge how novel this method is. If I understood correctly, the authors perform the analysis fully within the commercial software “FLUENT”, using their built-in tools. However, they pay extra attention in constructing the mesh. 

I have found the text fairly unclear in many aspects, for instance:

- The title utterly misguided me. The term "multi-scale global fluid domain" means something different to me. I can imagine, having read the text, that they refer to the turbulence model. However, they use the standard k-epsilon turbulence model. Instead, I was thinking on a model that explicitly considers more than one scale. Hence, including that in the title should make it clearer. Also, the authors do a couple of simulations: one with a "standard" geometry and another one with a double slit added. I cannot see how that can be described as "Characteristics analysis and optimization".

- The abstract should be fully rewritten. Sentences like “To solve these problems, we proposed an approach of global fluid domain 5 model is proposed for the performance analysis” are simply grammatically incorrect, and others like “In the process of bearing performance analysis, in the operating film thickness range, the average error of the simulated supporting capacity compared with the experiment is only 10.76%, better than theoretical calculation.” Miss a lot of context for them to be understood. 

- It would seem as if the main novelty is a new meshing scheme. However, it seems that the authors use a combination of standard meshing tools. Again, section 3.3 it is claimed that it is very difficult to used conventional methods to generate the mesh. However, it also seems that built in Fluent mesh operations are used. Can a meshing method in the most well-used comertial software be considered as "non-conventional"? While I agree with the authors about the need of carefully building the mesh and I wish that most works followed such care, I think the "novelty" of their approach is exaggerated

- A lot more explanation is needed around Figure 3. The bearing cannot be seen, as it is hiden by lots of accessories. These, however, are not discussed. 

- The derivations in section 2 are clearly not done by the authors. It is not clear what sources they are taken from. The authors should write something to give due credit. A similar comment applies to section 3

- In Section 3.2 it seems that a version of Reynolds transport theorem is given in eq 18. It is not clear to me how this equation used. What is the scalar? Then the scalar, as well as rho, then vanishes in eq 20 with no explanation. Then, in 21, it seems as if the whole RHS of eq. 18 is discarded and the fluid velocity is set to zero. While I am not saying that the formulation is incorrect, its justification is clearly lacking. 

- Regarding eq. 22 can we see how good or bad the fit is? Was this data obtained for this study or is it obtained from the literature?

- Experiments are reported very vaguelly. Can the authors provide a detailed explanation of the method use or a citation to a related previous work where such explanation is given? For instance, when, in Section 5, it is claimed that "the surface warps due to the constraint of the ball hinge on the upper surface", it is very hard to know what the authors are talking about. The readers should have at the very minimum, enough information to understand the claims made by the authors. 

- I could not guess what the authors tried to say with the second paragraph of section 5.

- Figure 9 is very hard to understand. What are the different colours? I guess they are projections, but it is not totally obvious. Also, are all the projections meaningful? In what manner is this 3D plot bringing more information than an easier to read 2D plot, (perhaps combining bearing force against time and Wall velocity against time in the same graph)?

- Regarding Fig. 10, and given that velocity and force oscillate while they damp, what values are exactly plotted?

- The authors claim that the results from figure 12 are consistent with those in fig. 5. Are not both results of the same model under similar conditions?

- In Figure 15a, I see vortices everywhere. These are even marked by the authors. However, the text (page 13, lines 284 onwards) says that no vortices are seen in some conditions. Where can I see that?

- The double slit approach seems promising. However, some discussion and perhaps extra simulations should be provided to showcase how and why it works so well, why was it expected to work, how does it improve in the stability, what effects does it have on the stiffness and damping, etc. In summary, we are told that vortices disappear without being told how the changes affect the actual performance of the bearing. In a complex system as the one studied by the authors a change may improve some issue while sacrificing some other characteristic. For instance, supressing vortices by having a very soft bearing might be detrimental for high precision applications. 

 

In summary, the work seems very promising, but it seems more an initial study to check for feasibility than a comple

 

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

See below my comments on the authro's response. My feeling is that they took an approach of keeping the changes to a bare minimum. 

Point 1:

The title now is more representative, but I would change the phrasing “on Meshing scheme” with by “on a XXX meshing scheme”, where the XXX informs a bit on the meshing scheme.

Point 2:

Ok

Point 3:

I complained about the mesh being overly emohasied as novel (when it used Standard CFD tools) in Sections 1 and 3.3. I did not see changes in those sections.

Point 4:

Now it is better. However, you use ball in the imatge and sphere in the text. Why not using the same word?

Point 5:

Ok

Point 6:

This section is still far from clear. If it is a complex topic, too long to be explained here, you can cite a source that explains it in detail and simplify your explanation. In the current form, it does not bring much. Some of the main issues I have are:

-          If eq (19) simply discretizes the first term, simply state it. Also note that the discretization provided is only valid for constant \rho and \phi. It is fine if this is the case, but then you must state it.

-          In eq (20), can we assume that (\rho\phi V)^{n+1} = \rho\phi(V^{n+1}). Should the density or the scalar not be constant, then this is not true at all.

-          The phrase “In order to ensure the grid conservation relationship,” is then confusing. Eq.  (18) is also a conservation law, while eq (21) only gives the computation needed to compute a single term.

-          If all the discussion is made to compute the first term, what happens with all others?

-          Also, there is little point in explaining it to me if it remains unclear in the article

Point 7:

The response does not answer the question at all. Saying that "First, oil is a power-law fluid, which was consistent with the power-law equation" amounts to say nothing. By definition, a power law fluid is described by a power-law equation. But this does not show that the fluid is a power law.

If you take it from the literature because it is a common one: cite.

In addition, you need to tell how the parameters are obtained. If not from experimental measurements, where are the values of k and n coming from? You are comparing your results with experiments. Surely, it is important that the fluid description and the parameters used to describe the model.

 

Point 8:

Ok

 

Point 9

It is mostly fine. However, what do you mean by “it is impossible to evaluate the difference of bearing stiffness obtained by each method through images”?

Point 10:

 

Point 10:

 

I still think that the figure is unclear: nothing has been changed in the figure nor in the caption.

Also, I do not understand why a 3D plot (always harder to read), needed

Point 11:

This is still very unclear.

 

If I understand it correctly, you are basically re-plotting the red curve in Fig. 9 (all the more reason not to have a 3d plot). Is this really the best way to compute the damping?

 

If I am right, "In all periods" does not represent the fact that you are basically plotting velocity and force at given time steps.

 

Point 12:

If the results in Fig. 12 are related to a simplified model, then where is the simplified model described? The first time the working “simplified model” appears is in Section 5.3, together with the results. What is changed from the un-simplified one? It does not make sense to validate the un-simplified version and then using the simplified one to obtain the results?

 

Point 13:

Ok

 

Point 14:

I cannot see how simply having a CFD model is novel enough. Moreover, if the use of slits was already known, what will the potential reader gain?

I see really no new discussion as compared to the previous version.

Author Response

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Author Response File: Author Response.pdf