Analytical Determination and Influence Analysis of Stiffness Matrix of Ball Bearing under Different Load Conditions

Round 1

Reviewer 1 Report

The article deals with the impact of various parameters on bearing stiffness. The presented material might be attractive for a broad international audience, particularly for specialists in rotor dynamics. However, it has the following flaws that should be eliminated:

1. In the literature review, most references (e.g., [2–6, 10–14, 20–28, 38–40]) are unacceptably outdated, and cannon be adequate in a critical literature review. Therefore, the authors should do a review with up-to-date studies in bearing stiffness from publications in the Scopus and Web of Science databases in the period of 2010–2022.
2. There is no main aim of the research in the text. Therefore, the conclusions are declarative.
3. The manuscript is poorly structured. In particular, formulas (1)–(26) should be placed as they appear in the text.
4. It seems the presented material was partially published previously in [42].
5. I do recommend that authors indicate the scientific novelty more transparently.
6. The discussion does not compare the obtained results with existing studies of other reputable publications in bearing stiffness.
7. There are no quantitative indicators of the aim’s achievement in the conclusions.

Overall, the article can be recommended for publication after a major revision according to the recommendations mentioned above.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Review of the manuscript  „machines-1620650 -Analytical determination and influence analysis of stiffness matrix of ball bearing under different load conditions”

 Dear authors,

A sophisticated theoretical model on the ball bearings’ stiffness for various geometry and operation conditions (loads and speeds) has been developed by the authors. The model is interesting and the simulated results suggest the influences of the  races curvatures on the ball bearing stiffness, correlated with loads and rotational speed.

Following comments and observations we indicate in order to increase the quality of your manuscript:

1.As a firs comment is reefer to the manuscript presentation. So, the equations are  written  at the end of manuscript  making it difficult to follow reasoning. Also, in text the relations must be indicated by Eq. (1), Eq. (2)…… no by (1), (2),….. 

2.Because the manuscript contain a lot of parameters we consider necessary to be included a Nomenclature .

3.Also, the figures must be included in the text, to be easy verified the concordance between text and parameters from figures.

4.In the paragraph 2.1 is indicated that “expressions K_ik and K_ok are given in Appendix. A” but Appendix A is not present in manuscript!

5. In the paragraph 3.1.3 are indicated the radius of inner and outer races by r_i and r_o and in bracket are indicated (fi) and (fo) respectively. Please explain that fi and fo are the conformity parameters with the following relations: fi,o=ri,o/D, where D is ball diameter.

6.The 5 components of the vector d ( three deformations and two rotations of the inner ring relative to the outer ring) must be explained and presented in Fig. 1 or in other figure.

7.In Fig. 2-b is not indicated the angle α_ik , also the figures 2-a and 2-b must be realized most clearly!

8.Your simulation graphics, from Fig. 5 to Fig.15, indicate the variation of the axial or radial stiffness of some ball bearings presented in Table 1.

9. In the ball-races contacts the stiffness or the rigidity is a ratio between applied force and deformation at power 3/2  (Q=K*δ^3/2 ). For entire ball bearing both in axial or radial direction exist a  nonlinear relation between force  and deformation. As consequence the unity of the stiffness  is not N/µm ( that means a linear correlations)! Is not clear for us if you obtained a linear correlation between force and deformation in axial or radial direction?

10. In Figs. 12 and 14 are not presented the variation of the initial contact angle as function of  race and ball diameter, but you presented  the positive or negative deviation (tolerances!) of race and ball diameter. Please give correct indications In many figures include correct “µm” instead of ”um”.

11.In Fig. 9 the variation of the axial and radial stiffness with radial load  not exceed 2.5% , and these results can be as precision of calculus. Practically, between  0 and 200N the stiffness variation can be ignored.

12.The Table 1 have a discontinuity. Please includes the types of preloads in a new Table 2 and explain what represent EL,L.M and H. Also, in the some table  the presentation is confuse: the stiffness determined by model and by the manual of company  must be clear separated.

13.Please indicate in Table 1 the initial contact angle of the tree ball bearings.

14 For all figures with simulated results please indicate the type of ball bearing  which you mean!

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors have made all the corrections thoroughly according to all the comments concerning the main aim, the scientific novelty, the discussion, the conclusions, and the general structure. Therefore, the article can be recommended for publication.

Reviewer 2 Report

Dear authors,

Thanks for all comments and for revision of my observation.

The revised version of manuscript has been important increase in quality.