Design and Experimental Research of a Non-Destructive Detection Device for High-Precision Cylindrical Roller Dynamic Unbalance

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper presents a non-invasive methodology to predict the unbalance grade of light rotors.
The proposed methodology exploits air bearings to reduce non-rotating damping. The unbalance is then predicted by measuring the lateral displacement of an air floatation guide.
The technique requires a fitting to the non-rotating damping of the device, which mainly depends on air pressure and airgap.

The paper writing style is discrete. It presents several typos and formalism issues which must be accounted through a deep proof editing.
The paper is well structured and is the author purposes are clear. Nevertheless, the points of novelty of the activity are vacuous.
The State-of-the-Art is not sufficient. It is basically not recent and the majority of the references are hard to obtain. It must be revised with more recent content of the last 5 years from significant sources.
Also, the conclusions should contain quantitative considerations.

The adopted methodology and terminology is not precise. The rotor longitudinal response on the air floatation guide is modelled as a SDOF system subject to static unbalance (eq 1) which is called in the whole paper "dynamic unbalance". The static unbalance concept is related to a variation of the radial amplitude of response due to the presence of an eccentricity, while dynamic unbalance is related to a certain angle between geometrical rotor axis and inertia axis.

Globally, this Reviewer considers the manuscript suitable for publication after major revision of the paper and the following corrections.

1) please, reconsider the usage of "static unbalance" instead of "dynamic unbalance" in the whole manuscript (title, abstract, keywords, main text). It follows the common terminology used in rotordynamics and also referred in many textbooks:
    Giancarlo Genta, Dynamics of Rotating Systems, Springer New York, NY, 2005, https://doi.org/10.1007/0-387-28687-X

2) the usage of laser displacement sensors and speed tachometer is an already adopted procedure from other students worldwide. I suggest the authors to revise the State-of-the-Art to better recognise these results. Here some recent readings which can be used by the authors to improve their introduction:
    Bagaric I., Steinert D., Nussbaumer T., Kolar J.W. "Supercritical Operation of Bearingless Cross-Flow Fan", Machines 2024, 12, 223, https://doi.org/10.3390/machines12040223
    Venturini S. et al., "Experimental Techniques for Flywheel Energy Storage System Self-discharge Characterisation", Mechanisms and Machine Science, 164, 2024, https://doi.org/10.1007/978-3-031-64569-3_22
    Bonisoli E. et al., “Nonlinear characterisation of a rotor on passive magnetic supports”, International Journal of Mechanics and Control, 23 (1): 121-128, 2022
    Jin X., Liu Y., "Numerical and Experimental Analysis for the Dynamics of Flawed–Machining Rod–Disk Rotor with Inner Misalignment", Machines 2022, 10, 355, https://doi.org/10.3390/machines10050355

3) line 166: substitute "resistance coefficient" with "damping coefficient"

4) it is better to express the eq 3 as a function of the rotating vector x + iz and then isolate the longitudinal component in the response in eq5.

5) Symbol "m" in Figure 3, is not consistent with "M" in the equations. Please, also reconsider the usage of epsilon only for eccentricity, and not also for phase angle in eq 5.

6) line 232: substitute "orders of the vibration" with "modeshapes"

7) line 247: please, specify the type of damping is introduced in the model. Viscous-proportional? Proportional to mass, stiffness?

8) Figure 6b should emphasise the amplitude of response mangitude after and before the critical speed. I suggest to use log scale for the displacement.

9) line 327: please correct "Mpa" with "MPa" in the whole text.

10) how did you excited the rotor? Constant angular speed or ramp? Does this choice interfere with your modeling procedure?

 

 

Comments on the Quality of English Language

The paper writing style is discrete. It presents several typos and formalism issues which must be accounted through a deep proof editing.

Please, consider the list of comments int the previous section.

Author Response

Response to Reviewer 1 Comments

 

Dear reviewers:

Thank you for your kindly reviewing our paper titled “Design and Experimental Research of Non-destructive Detec-tion Device for High Precision Cylindrical Roller Dynamic Unbalance”. The list of the revisions in accordance with your comments is as follows.

 

Point 1: please, reconsider the usage of "static unbalance" instead of "dynamic unbalance" in the whole manuscript (title, abstract, keywords, main text). It follows the common terminology used in rotordynamics and also referred in many textbooks:

Response 1: Thank you very much for your comments. We generally agree that static unbalance refers to the phenomenon exhibited by a non-rotating object, such as an unbalanced lever. Dynamic unbalance, on the other hand, refers to the phenomenon observed in a rotating body when the axis of rotation does not coincide with the axis of the geometric center during rotational motion. The asymmetry of the shape of the rotating body and the non-uniformity of the material cause the rotating body to produce 'unbalance' in its motion, which we will refer to as dynamic unbalance. The definition of dynamic unbalance varies by region, and the definition used in this paper is widely accepted in the literature. This paper employs the term dynamic unbalance based on numerous references. If we were to change it to static unbalance, these references would become irrelevant. Therefore, we cannot make corresponding changes in the manuscript. I apologize for any inconvenience.

 

 

Point 2: the usage of laser displacement sensors and speed tachometer is an already adopted procedure from other students worldwide. I suggest the authors to revise the State-of-the-Art to better recognise these results. Here some recent readings which can be used by the authors to improve their introduction:

Response 2: Additional notes on laser displacement sensor and laser tachometer have been added to the manuscript for your review.

 

 

Point 3: line 166: substitute "resistance coefficient" with "damping coefficient"

Response 3: The relevant changes have been reflected in the manuscript, so please check it out..

 

 

Point 4: it is better to express the eq 3 as a function of the rotating vector x + iz and then isolate the longitudinal component in the response in eq5.

Response 4: Equations 3 and 5 are from the textbook Theoretical Mechanics and are well-established and widely used formulas.

 

Point 5: Symbol "m" in Figure 3, is not consistent with "M" in the equations. Please, also reconsider the usage of epsilon only for eccentricity, and not also for phase angle in eq 5.

Response 5:is the vibration system mass, is the eccentric mass of the cylindrical roller,  is the mass eccentricity distance,  is the phase angle.

 

 

Point 6: line 232: substitute "orders of the vibration" with "modeshapes"

Response 6: Thank you very much for your comments, the corresponding position in the manuscript has been revised.

 

 

Point 7: line 247: please, specify the type of damping is introduced in the model. Viscous-proportional? Proportional to mass, stiffness?

Response 7: The harmonic response analysis uses a Damping Ratio model with a damping ratio of 0.02. The purpose of the harmonic response analysis is only to verify the feasibility of the device proposed in this paper, not to do an accurate quantitative analysis, so the harmonic response analysis is not accurate.

 

 

Point 8: Figure 6b should emphasise the amplitude of response mangitude after and before the critical speed. I suggest to use log scale for the displacement.

Response 8: Figure 6b expresses the amplitude of the vibrating system at resonance, which is not infinitely large due to damping and therefore does not need to be expressed using a log scale. The purpose of Figure 6b is to emphasize that the amplitude of a vibrating system is significantly higher at resonance compared to other times. By exploiting the amplifying effect of resonance, it is possible to dramatically enhance small vibration signals caused by unbalance.

 

 

Point 9: line 327: please correct "Mpa" with "MPa" in the whole text.

Response 9: Thank you very much for your comments, I have made the change in the corresponding place in the manuscript, please check it out.

 

 

Point 10: how did you excited the rotor? Constant angular speed or ramp? Does this choice interfere with your modeling procedure?

Response 10: The air flotation sleeve is securely affixed to the air flotation slide, facilitating the introduction of compressed air into the sleeve, thus generating an air film. Initially, the cylindrical roller remains stationary within the air flotation sleeve, with the air film solely shouldering the roller's self-weight. Subsequently, the electric spindle descends axially along the cylindrical roller, resulting in a reduction in air film thickness and an attendant increase in load-bearing capacity. The air flotation electrical spindle harnesses the static frictional force exerted by the vacuum suction cup on the upper surface of the cylindrical roller to initiate high-speed rotation. Once the predetermined speed is achieved, the electric spindle ascends, disengaging the vacuum suction cup from the upper surface of the cylindrical roller. Consequently, the cylindrical roller commences independent rotation within the air flotation sleeve, embarking on the dynamic unbalance detection process. Please refer to reference [26] for specific content details.

 

26. Liang, S.; Duan, M.; Zhang, Z. Development and Investigation of Non-Destructive Detection Drive Mechanism for Precision Type Cylindrical Roller Dynamic Unbalance. Applied Sciences. 2023, 13(24): 13266.

 

Comments on the Quality of English Language: The paper writing style is discrete. It presents several typos and formalism issues which must be accounted through a deep proof editing. Please, consider the list of comments int the previous section.

Response: Thank you very much for your comment, I have carefully proofread the entire text and made corrections to grammar, formatting and other issues, please check it out.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

1.        Micro dynamic unbalance problem is one of the key factors affecting the performance of the precision cylindrical roller and service life of rolling bearings. This paper proposes a new detection method, establishes a dynamic model of the vibration system, and carries out modal analysis and harmonic response analysis of the vibration system, and the analytical results show that the detection device can detect the micro dynamic unbalance of the cylindrical roller. The novel idea in this paper is the application of non-destructive method to detect the unbalance data of cylindrical rollers. 

Basically, the results do agree with the purpose of the research.

2.        The English has to be edited thoroughly. For example, “At present, the common dynamic balancing machines at home and abroad are mainly for automobile wheel hubs, machine tool …. Line 50.” And “the sentence is not complete. Line 80,”, the sentences are not consistent grammarly. The bibliography is fine.

3.        In line 87, what is the definition of high stiffness of the air film? Air film is not supposed “stiff”. How the stiffness coefficients of the air film and the spring damping coefficient are chosen in the modal simulation?

4.        Physical definition of the dynamic unbalance U? What is the object (or physical quantity) of the sensor detection? (acceleration ?) In eqn.1, U is the measured force on the roller? The eqn.1 has to be explained in more detail, since it seems to be proportional to the square of rotation speed.

5.        The method uses optical sensing, thus, it’s non-destructive. However, the experimental setup does not have to be called non-destructive though, or it may be called non-contact.

6.        There are other means of gap detection e.g., imbedded capacitive gap sensor. Can the authors do a little literature survey in the introduction section?

7.        In Fig. 12, what causes the different response between roller 0 (no load?) and 2? Since it’s quite obvious.

8.        The Fig. 13 is actually the linear regression of the data by eqn. 11. The caption may as well be written as that.

Comments on the Quality of English Language

1.        Micro dynamic unbalance problem is one of the key factors affecting the performance of the precision cylindrical roller and service life of rolling bearings. This paper proposes a new detection method, establishes a dynamic model of the vibration system, and carries out modal analysis and harmonic response analysis of the vibration system, and the analytical results show that the detection device can detect the micro dynamic unbalance of the cylindrical roller. The novel idea in this paper is the application of non-destructive method to detect the unbalance data of cylindrical rollers. 

Basically, the results do agree with the purpose of the research.

2.        The English has to be edited thoroughly. For example, “At present, the common dynamic balancing machines at home and abroad are mainly for automobile wheel hubs, machine tool …. Line 50.” And “the sentence is not complete. Line 80,”, the sentences are not consistent grammarly. The bibliography is fine.

3.        In line 87, what is the definition of high stiffness of the air film? Air film is not supposed “stiff”. How the stiffness coefficients of the air film and the spring damping coefficient are chosen in the modal simulation?

4.        Physical definition of the dynamic unbalance U? What is the object (or physical quantity) of the sensor detection? (acceleration ?) In eqn.1, U is the measured force on the roller? The eqn.1 has to be explained in more detail, since it seems to be proportional to the square of rotation speed.

5.        The method uses optical sensing, thus, it’s non-destructive. However, the experimental setup does not have to be called non-destructive though, or it may be called non-contact.

6.        There are other means of gap detection e.g., imbedded capacitive gap sensor. Can the authors do a little literature survey in the introduction section?

7.        In Fig. 12, what causes the different response between roller 0 (no load?) and 2? Since it’s quite obvious.

8.        The Fig. 13 is actually the linear regression of the data by eqn. 11. The caption may as well be written as that.

Author Response

Response to Reviewer 2 Comments

 

Dear reviewers:

Thank you for your kindly reviewing our paper titled “Design and Experimental Research of Non-destructive Detec-tion Device for High Precision Cylindrical Roller Dynamic Unbalance”. The list of the revisions in accordance with your comments is as follows.

 

 

Point 2: The English has to be edited thoroughly. For example, “At present, the common dynamic balancing machines at home and abroad are mainly for automobile wheel hubs, machine tool …. Line 50.” And “the sentence is not complete. Line 80,”, the sentences are not consistent grammarly. The bibliography is fine.

Response 2: Thank you very much for your comment, I have made changes to address the issues you raised, please check them out. In addition I have carefully proofread the entire text and made corrections to grammar, formatting, and presentation.

“Currently, common dynamic balancing machines, both domestically and internationally, are primarily designed for large-volume and high-mass rotary bodies such as automobile wheel hubs, machine tool spindles, and motor rotors. In contrast, cylindrical rollers, which have relatively smaller volume and mass, present challenges in dynamic unbalance detection. Issues such as detection difficulties and the risk of damaging the surface during detection are more prevalent with these smaller components.”

“Yong Cui et al. [21,22] and Xin Sui et al. [23] from Henan University of Science and Technology designed a MEMS-based detection system for dynamic unbalance in small-mass cylindrical rollers. This system uses V-block support and a pulley drive to address issues associated with traditional detection systems, such as large swing frame mass, high cost, and low sensitivity.”

 

 

Point 3: In line 87, what is the definition of high stiffness of the air film? Air film is not supposed “stiff”. How the stiffness coefficients of the air film and the spring damping coefficient are chosen in the modal simulation?

Response 3: Air flotation equipment typically has a very high bearing capacity, while the thickness of the air film responsible for bearing is very small, usually around tens of microns. As a result, the air film has much greater stiffness compared to a spring. In this study, the stiffness coefficient of the air film only needs to be significantly larger than that of the spring; detailed information can be found in the following references. The damping coefficient of the spring should be as low as possible, and a spring with a damping coefficient of 0.02 was chosen for this study.

 

 

Point 4: Physical definition of the dynamic unbalance U? What is the object (or physical quantity) of the sensor detection? (acceleration ?) In eqn.1, U is the measured force on the roller? The eqn.1 has to be explained in more detail, since it seems to be proportional to the square of rotation speed.

Response 4: The physical definition of dynamic unbalance is the product of the eccentric mass of the rotating body and the eccentric distance. The transducer detects displacement in millimeters, with a resolution of 0.0001 mm and a range of ±0.5 mm. Equation 1, which is from the textbook Theoretical Mechanics, shows that the centrifugal force  is indeed proportional to the square of the rotational speed.

 

Point 5: The method uses optical sensing, thus, it’s non-destructive. However, the experimental setup does not have to be called non-destructive though, or it may be called non-contact.

Response 5: In this study, the term ‘non-destructive’ refers to the fact that the device proposed for detecting cylindrical rollers does so without causing damage. The non-contact nature of the sensors is a necessary measure to ensure this non-destructive capability

 

 

Point 6: There are other means of gap detection e.g., imbedded capacitive gap sensor. Can the authors do a little literature survey in the introduction section?

Response 6: The thickness of the air film (gap) is very small, making it difficult to detect directly. This paper does not address the measurement of the air film thickness in detail, as it is only required to meet the testing requirements. For the design of the air film thickness, there are established design manuals. Please refer to the following references for more details.

  Liu, D.; Liu, Y.; Chen, S. Hydrostatic gas lubrication, 1st ed.; Harbin Institute of Technology: Harbin, China,1990; pp. 51-121.

 

 

Point 7: In Fig. 12, what causes the different response between roller 0 (no load?) and 2? Since it’s quite obvious.

Response 7: Cylindrical roller 0 was used as a control test sample and was not artificially de-weighted, so it has no dynamic unbalance. Consequently, the cylindrical roller without dynamic unbalance produces almost no vibration signals during motion, resulting in it appearing as a straight line in the figure. In contrast, cylindrical roller 2 was artificially de-weighted to introduce dynamic unbalance. The centrifugal force due to the unbalanced mass (as described by Equation 1) caused the vibration system to generate significant amplitude during rotational motion.

 

 

Point 8: The Fig. 13 is actually the linear regression of the data by eqn. 11. The caption may as well be written as that.

Response 8: Thank you very much for your advice.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The abstract needs a better description of the system and clarification of the type of rollers the authors are dealing with.

The English writing needs important improvements.

Introduction.

Eliminate those paragraphs that are too general.

The references are impossible to read; they must only include references in English. The paper lacks an analysis of the references versus the proposed method.

Detection device

The authors did not present any theoretical or experimental results that support the design assumptions.

All the equations correspond to a well-known DOF system.

Simulation

The simulation results are not related to any bearing prototype.

Test

There is no calibration analysis, the device cannot be reproduced, and the data cannot be related to any other analysis technique.

There is no sensitivity analysis.

Author Response

Response to Reviewer 3 Comments

 

Dear reviewers:

Thank you for your kindly reviewing our paper titled “Design and Experimental Research of Non-destructive Detec-tion Device for High Precision Cylindrical Roller Dynamic Unbalance”. The list of the revisions in accordance with your comments is as follows.

 

 

Point 1: The abstract needs a better description of the system and clarification of the type of rollers the authors are dealing with.

Response 1: Thank you very much for your comment, I have rewritten the summary section, please check it out.

“Due to their small size and light mass, small precision cylindrical rollers present challenges in dynamic unbalance detection, including difficulties in measurement and the risk of surface damage. This paper proposes a non-destructive detection device for assessing the dynamic unbalance of small precision cylindrical rollers. The device utilizes an air flotation support method combined with resonance amplification to indirectly measure the dynamic unbalance. A dynamic model of the air flotation tooling-cylindrical roller vibration system was developed to explore the relationship between the vibration parameters of the air flotation tooling and the dynamic unbalance of the cylindrical roller. Modal analysis and harmonic response analysis were performed, revealing that the amplitude of the vibration system at resonance could be detected using the sensor. Additionally, modal testing was conducted to determine the natural frequency of the system. A non-destructive detection platform was constructed for testing the dynamic unbalance of cylindrical rollers. Microscopic observation of the roller surface before and after testing confirmed that the device successfully performs non-destructive detection of dynamic unbalance.”

 

 

Point 2: The English writing needs important improvements.

Response 2: Thank you very much for your comment, I have carefully proofread the full manuscript, corrected as many grammatical errors as possible and optimised the presentation of the statements to make the article more readable. Please check it out.

 

 

Point 3: Introduction.

Response 3: I have made a number of changes and optimisations to the introduction section, refining the language and adopting a more formal and academic tone to enhance readability and coherence.

 

 

Point 4: Eliminate those paragraphs that are too general.

Response 4: Thank you very much for your comment!

 

 

Point 5: The references are impossible to read; they must only include references in English. The paper lacks an analysis of the references versus the proposed method.

Response 5: Currently, there is a paucity of research on the detection of dynamic unbalance in cylindrical rollers, with our team being one of the few conducting investigations in this area. Consequently, relevant references are scarce.

 

 

Point 7: Detection device. The authors did not present any theoretical or experimental results that support the design assumptions.

Response 7: This research is primarily design-oriented, focusing on achieving the functional objectives of the proposed design.

We have proposed a non-destructive detection device for the dynamic unbalance of cylindrical rollers with precision type small mass cylindrical rollers and indirectly obtain the dynamic unbalance of cylindrical rollers by using air flotation non-destructive support method and resonance amplification effect, while ensuring almost no damage to its surface.

 

 

Point 8: All the equations correspond to a well-known DOF system.

Response 8: The formulas employed in this paper are derived from standard theoretical mechanics textbooks and are widely utilized in the field.

 

Point 9: Simulation. The simulation results are not related to any bearing prototype.

Response 10: The simulation results presented in this study are specifically applicable to the dynamic unbalance detection device developed herein.

 

 

Point 11: Test. There is no calibration analysis, the device cannot be reproduced, and the data cannot be related to any other analysis technique.

Response 12: The dynamic unbalance detection device introduced in this study is distinct in its design and does not have a comparable counterpart in the market, underscoring its high level of innovation.

 

 

Point 13: There is no sensitivity analysis.

Response 13: Sensitivity analysis is being explored by other members of our research team. This aspect of the study is currently being led by a senior colleague and will be submitted to your journal in the near future. We look forward to your valuable feedback.

 

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

I have a few comments about the way the results are presented, the modeling, the vocabulary used. I will address these aspects in the following paragraphs.

1. the first comment concerns FEM modeling. Classically, an FEM model is built in an iterative process using experimental results. The article does not provide any details on how FEM model is modeled, the type of finite elements, the boundary conditions. Looking at the values of the eigenfrequencies, one can have doubts about their correctness, since the first one is about 19 Hz, and the next one is already about 1091 Hz. Nothing between? I can guess that the first one is related to the motion of the rigid body, but the general observation is that it is actually not clear for what purpose they are presented. The model is not validated. The sentence starting at line 300 as if the eigenfrequency of the system is at 18.32 Hz does not bring any relevant information, it is not known what form of vibration it is and what actually everything is for.

In summary, if the experimental research was used to update the FEM model - please demonstrate this in the article. As it stands, Chapter 3 is practically useless.

 

2.The practical part needs clarification. The software used and the measuring equipment should be described in more detail. I am not accusing the authors of anything here except incomplete information. As a practitioner of modal analysis, I have never encountered such sensors or software. In addition, I disagree with the statement in line 296 that about 5% of the mass of the whole object, is an insignificant mass of the sensor. My practice indicates that if the sensor is 5% of the object's mass - it significantly disturbs the object's mode shapes. Commercially, much lighter sensors or non-contact methods are available.

I believe that this chapter should be supplemented with the mentioned information and additional analysis, confirming the lack of influence of the mass of the sensor on the form of vibrations.

3. section 4.2 uses the phrase (line 312) “specification close to the same” In scientific articles, such expressing is unacceptable. Another question is how to determine the unbalance. It is given with a precision of up to 5 digits. Please describe and explain this in more detail.

 

Figure 11 shows the sensor indications in mm. An acceleration sensor was used. How were the values in Figure 11 determined?  How to understand the waveforms if the rotation is 6000 rpm and here we have some, strange in my opinion, waveform as a function of time, where the time has a value of 18 seconds? Please explain this graph and describe what it was used for.

Line 353 - what do the authors mean by test stability?

Table 2 gives values with an order of E-03 micrometers. Why such precision?

Line 376 - Values of regression coefficients are given with confidence intervals? What does it mean to say that since the “variance of the function” is greater than 0.9 the fit is “better”? From what, what is the variance? Please rework your findings and present them in a readable form.

 

According to the authors, what is the difference between resistance (line 159, 160 and several others) and damping?

I don't understand the message/sense of the sentence in lines 255-257. Please clarify or rephrase it for better comprehensibility.

Comments on the Quality of English Language

4. spelling and vocabulary.

Please structure your citations in the text. Sometimes there are spaces, sometimes there are none, sometimes there is a period, sometimes there is not.

 

Author Response

Response to Reviewer 4 Comments

 

Dear reviewers:

Thank you for your kindly reviewing our paper titled “Design and Experimental Research of Non-destructive Detection Device for High Precision Cylindrical Roller Dynamic Unbalance”. The list of the revisions in accordance with your comments is as follows.

 

 

Point 1: the first comment concerns FEM modeling. Classically, an FEM model is built in an iterative process using experimental results. The article does not provide any details on how FEM model is modeled, the type of finite elements, the boundary conditions. Looking at the values of the eigenfrequencies, one can have doubts about their correctness, since the first one is about 19 Hz, and the next one is already about 1091 Hz. Nothing between? I can guess that the first one is related to the motion of the rigid body, but the general observation is that it is actually not clear for what purpose they are presented. The model is not validated. The sentence starting at line 300 as if the eigenfrequency of the system is at 18.32 Hz does not bring any relevant information, it is not known what form of vibration it is and what actually everything is for

In summary, if the experimental research was used to update the FEM model - please demonstrate this in the article. As it stands, Chapter 3 is practically useless.

Response 1: The finite element model used in this study is derived from the device described in Chapter 2, which provides a detailed account of its structural components. The vibration system comprises a detection rod, air flotation slide, air flotation sleeve, cylindrical roller, and springs. The air flotation guide constrains the five degrees of freedom of the air flotation slide, allowing it to move freely along the x-axis. When the cylindrical roller rotates within the air flotation sleeve, it induces movement of the vibration system along the x-axis. The fundamental frequency corresponds to the x-direction. Due to the lack of constraints from the air flotation guide in the x-direction, with only the spring providing support, the modal frequency of the vibration system (including the air flotation slide) in the x-direction is significantly lower than that in other directions.

  The core innovation of this study lies in the following: When a cylindrical roller with dynamic unbalance rotates, it generates centrifugal forces. If these centrifugal forces match the natural frequency of the vibration system, resonance occurs, significantly amplifying the vibration signals caused by the dynamic unbalance, thereby achieving the detection objective. Therefore, it is essential to ascertain the natural frequency of the vibration system. Chapter 3 aims to identify the vibration modes of the system and to evaluate the feasibility of the proposed method through harmonic response analysis. In Chapter 4, modal testing determined the actual natural frequency of the vibration system to be 18.32 Hz, further validating the feasibility of the proposed approach.

 

 

Point 2: The practical part needs clarification. The software used and the measuring equipment should be described in more detail. I am not accusing the authors of anything here except incomplete information. As a practitioner of modal analysis, I have never encountered such sensors or software. In addition, I disagree with the statement in line 296 that about 5% of the mass of the whole object, is an insignificant mass of the sensor. My practice indicates that if the sensor is 5% of the object's mass - it significantly disturbs the object's mode shapes. Commercially, much lighter sensors or non-contact methods are available.

  I believe that this chapter should be supplemented with the mentioned information and additional analysis, confirming the lack of influence of the mass of the sensor on the form of vibrations.

Response 2: The introduction of the modal testing equipment and the detailed testing procedures would significantly lengthen the manuscript. The modal testing equipment used is not uncommon and is widely employed in the NVH (Noise, Vibration, and Harshness) testing field within the automotive industry. I have provided additional explanations regarding the modal testing content for your review; however, due to length considerations, this material will not be included in the main text. While the quality of the sensors can indeed influence the modal shapes, the objective of this experiment is merely to determine the approximate natural frequency of the vibration system, rather than obtaining highly precise data. Therefore, the interference introduced by the sensors is considered acceptable.

The accelerometer and data acquisition analyzer (PREMAX) are connected to their respective channels. The force hammer is connected to the input channel of the data acquisition analyzer through a charge amplifier (YE5852). The data acquisition analyzer is then connected to the computer via a gigabit Ethernet port. After completing the hardware connections, the Text EngineX software is launched, and the modal data acquisition module is selected. In the hardware parameters, the number of channels is set to 4, the excitation point coupling mode is set to AC single-ended, the measurement point coupling mode is set to IEPE, and the sensor types are specified as force and accelerometers. The sensitivity of the force sensor is set to 4.23 mV/(N), and the sensitivities of the accelerometers are set to 99.3 mV/(G), 100.3 mV/(G), and 99.6 mV/(G), respectively. Based on the finite element analysis results, the natural frequency of the vibration system’s vibration direction ranges from 0 to 30 Hz. Typically, the analysis bandwidth should be 3 to 5 times larger or more than this range. Therefore, the analysis bandwidth is set to 500 Hz with a sampling frequency of 1280 Hz. In the test point settings, the test method is configured as impact excitation, with the excitation channel set to -X and the response point directions set to +X, +Y, and +Z. Once the software is prepared, the compressor is turned on to supply air to the air flotation device, allowing the air flotation slide to be in a floating state within the static air flotation guide. The excitation point is struck with appropriate force, and the collected results are checked to ensure that the excitation signal has only one peak and that the frequency response curve is smooth. The process is repeated three times by clicking the “Next Frame” button, averaging the collected results. The collected time-domain signal from the force hammer and the vibration frequency response function are shown in Figures 1 and 2.

Figure 1 Time-domain signal

Figure 2 Vibration frequency response function

Before analysis, it is necessary to determine a series of critical node coordinates based on the vibration system information. A three-dimensional perspective wireframe diagram is created in Modal Genius software, with the measurement points marked according to their locations. To facilitate the software calculations, structural elements that have minimal impact on the results, such as the detection rod, are omitted. The constructed three-dimensional perspective wireframe diagram is shown in Figure 3.

Figure 3 3D perspective wireframe diagram

The collected frequency response functions are imported into the analysis software. Based on the geometric configuration of the structure and the parameter identification results, information such as frequency is obtained. Additionally, the vibration modes are displayed in a three-dimensional animated format.

After collecting modal data using Text EngineX software, the acquired data is imported into Modal Genius software for analysis. Based on the modal parameter analysis and calculations conducted by the software, the first-order natural frequency of the system is determined to be 18.32 Hz with a stiffness coefficient of 2.2525 N/mm. This chapter primarily focuses on the modal characteristics of the air flotation slide, with the first-order mode shape extracted as shown in Figure 4, including both the axial and Z-direction views. By comparing the mode shapes and frequencies, it is observed that the first-order frequency corresponds to the natural vibration frequency of the system along the length of the guide rail (X-direction).

Figure 4 First-order mode shapes

 

 

Point 3: section 4.2 uses the phrase (line 312) “specification close to the same” In scientific articles, such expressing is unacceptable. Another question is how to determine the unbalance. It is given with a precision of up to 5 digits. Please describe and explain this in more detail.

 

Figure 11 shows the sensor indications in mm. An acceleration sensor was used. How were the values in Figure 11 determined?  How to understand the waveforms if the rotation is 6000 rpm and here we have some, strange in my opinion, waveform as a function of time, where the time has a value of 18 seconds? Please explain this graph and describe what it was used for.

 

Line 353 - what do the authors mean by test stability?

 

Table 2 gives values with an order of E-03 micrometers. Why such precision?

 

Line 376 - Values of regression coefficients are given with confidence intervals? What does it mean to say that since the “variance of the function” is greater than 0.9 the fit is “better”? From what, what is the variance? Please rework your findings and present them in a readable form.

 

According to the authors, what is the difference between resistance (line 159, 160 and several others) and damping?

 

I don't understand the message/sense of the sentence in lines 255-257. Please clarify or rephrase it for better comprehensibility.

Response 3: Thank you very much for your comment, a correction has been made at the corresponding position in the article, please check it out. The product of the de-weighted mass and the eccentricity is the dynamic unbalance. The value obtained by the product operation we have kept five digits after the decimal point.

    Figure 11 uses a laser displacement sensor with an accuracy of 0.0001 mm. the cylindrical roller is accelerated to 6000 rpm, after which the cylindrical roller undergoes a free decay of speed in the air flotation sleeve, and resonates when the speed is reduced to a frequency close to that of the natural frequency of the vibration system (18.32 Hz), at which point a significant amplitude is detected by the laser displacement sensor. It takes some time for the speed of the cylindrical roller to decrease from 6000rpm to the resonance speed, so there is a period of time on both sides of the resonance point (12s) when the amplitude value is significantly smaller than the resonance point amplitude. Concerning the speed of 6000 rpm: this speed can of course be higher or lower, which only slows down or speeds up the time to the resonance point.

Testing the stability of the vibration system ensures that similar dynamic unbalance is detected every time the same cylindrical roller is tested.

The effective accuracy of the laser displacement sensor is 0.0001mm, and the fifth decimal digit is an estimate for reference only.

Figure 13 is a further elaboration of Figure 12, and in addition the research of this paper centres on the fact that the present detection device is capable of detecting a small dynamic unbalance of a cylindrical roller with a certain degree of accuracy and stability. We are currently in the process of conducting an in-depth study on accuracy and stability and apologise for not being able to show you more of our research results at this stage. We would like to present the results of our in-depth research to your journal in the future, so please keep an eye out for them.

This is a matter of our language expression, which has been corrected in the text.

The corresponding position in the text has been changed, so please check it out.

 

 

Point 4: spelling and vocabulary. Please structure your citations in the text. Sometimes there are spaces, sometimes there are none, sometimes there is a period, sometimes there is not.

Response 4: Thank you very much for your comment, I have carefully proofread for formatting issues, please check it out.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

1) The usage of dynamic unbalance terminology by the authors must be contextualised by citing the adopted manual, since to this reviewer it is unkown the adopted definition.

2) As stated in the previous reviewer comment, the State-of-the-Art is not sufficient. It is basically not recent and the majority of the references are hard to obtain. It must be revised with more recent content of the last 5 years from significant sources. For example, the usage of laser displacement sensors and speed tachometer is an already adopted procedure from other students worldwide. I suggest the authors to revise the State-of-the-Art to better recognise these results. Here some recent readings which can be used by the authors to improve their introduction:
    Venturini S. et al., "Experimental Techniques for Flywheel Energy Storage System Self-discharge Characterisation", Mechanisms and Machine Science, 164, 2024, https://doi.org/10.1007/978-3-031-64569-3_22
    Jin X., Liu Y., "Numerical and Experimental Analysis for the Dynamics of Flawed–Machining Rod–Disk Rotor with Inner Misalignment", Machines 2022, 10, 355, https://doi.org/10.3390/machines10050355

Author Response

Point 1: The usage of dynamic unbalance terminology by the authors must be contextualised by citing the adopted manual, since to this reviewer it is unkown the adopted definition.

Response 1: Thank you very much for your comments. Dynamic unbalance is defined in reference [6], which has been cited where ‘dynamic unbalance’ first appears, so please check it out.

6. Cui, Y.; Deng, S.; Niu, R.; Chen, G. Vibration effect analysis of roller dynamic unbalance on the cage of high-speed cylindrical roller bearing. Journal of Sound and Vibration. 2018, 434: 314-335.

 

 

Point 2: As stated in the previous reviewer comment, the State-of-the-Art is not sufficient. It is basically not recent and the majority of the references are hard to obtain. It must be revised with more recent content of the last 5 years from significant sources. For example, the usage of laser displacement sensors and speed tachometer is an already adopted procedure from other students worldwide. I suggest the authors to revise the State-of-the-Art to better recognise these results. Here some recent readings which can be used by the authors to improve their introduction:

Response 2: Thank you very much for your comments. The references have been changed considerably and, as far as possible, the most relevant and up-to-date English-language references have been used, so please check them out. In addition, the expressions ‘laser displacement sensors’ and ‘tachometers’ have been supplemented by references to the references provided by you.

1. He, C.; Zhang, J.; Geng, K.; Wang, S.; Luo, M.; Zhang, X.; Ren, C. Advances in ultra-precision machining of bearing rolling elements. The International journal of advanced manufacturing technology. 2022, 122:3493-3524.
2. Xu, F.; Ding, N.; Li, N.; Liu, L.; Hou, N.; Xu, N.; Chen, X. A review of bearing failure Modes, mechanisms and causes. Engineering Failure Analysis. 2023,
3. Li, X.; Horie, M.; Kagawa, T. Study on the basic characteristics of a vortex bearing element. The International Journal of Advanced Manufacturing Technology. 2013, 64:1-12.
4. Wang, D.; Yuan, J.; Hu, L.; Lyu, B. Multidimensional study on the wear of high-speed, high-temperature, heavy-load bearings. Materials. 2023, 16(7), 2714.
5. Hou, X.; Diao, Q.; Liu, Y.; Liu, C.; Zhang, Z.; Tao, C. Failure Analysis of a Cylindrical Roller Bearing Caused by Excessive Tightening Axial Force. Machines. 2022, 10(5), 322.
6. Cui, Y.; Deng, S.; Niu, R.; Chen, G. Vibration effect analysis of roller dynamic unbalance on the cage of high-speed cylindrical roller bearing. Journal of Sound and Vibration. 2018, 434: 314-335.
7. Tiwari, R.; Chakravarthy, V. Simultaneous estimation of the residual unbalance and bearing dynamic parameters from the experimental data in a rotor-bearing system. Mechanism and Machine Theory. 2009, 44(4), 792-812.
8. Harsha, S. P. Nonlinear dynamic analysis of an unbalanced rotor supported by roller bearing. Chaos, Solitons & Fractals. 2005, 26(1), 47-66.
9. Wang, A.; Yao, W. Theoretical and numerical studies on simultaneous identification of rotor unbalance and sixteen dynamic coefficients of two bearings considering unbalance responses. International Journal of Control, Automation and Systems. 2022, 20(6), 1971-2007.
10. Therale, L. Dynamic balancing of rotating machinery in the field. ASME Journal of Applied Mechanics. 1934, 56: 745-753.
11. Baker, G. Methods of rotor-unbalance determination. ASME Journal of Applied Mechanics. 1939, 61: A1-A6.
12. Zhang, X.; Jiao, H.; Hu, D.; Research progress on field dynamic balancing methods for rotating machinery. Journal of Mechanical and Electrical Engineering. 2021, 38(11): 1367-1377 (in Chinese).
13. Zhang, L.; Duan, Z.; Li, D. Research progress of on-site dynamic balancing technology. Chemical Engineering and Machinery. 2012, 39(06): 690-694 (in Chinese).
14. Louis, Two-plane balancing of a rotor system without phase response measurements. Transactions of the ASME, Journal of Vibration, Acoustics, Stress,and Reliability in Design. 1987, 109(2): 162-167.
15. Bishop, E. D.; Gladwell, G. M. L. The Vibration and Balancing of an Unbalanced Flexible Rotor. Journal of mechanical Engineering science. 1959, 1(1): 66-70.
16. Zou, D.; Zhao, H.; Liu, G. Application of augmented Kalman filter to identify unbalance load of rotor-bearing system: Theory and experiment. Journal of Sound and Vibration. 2019, 463: 68-69.
17. Parkinson, G. Balancing of rotating machinery. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. 1991, 205(1): 61-63.
18. Kellenberger, Should a flexible rotor be balanced in N or (N+2) planes. Journal of Engineering for Industry. 1972, 94(2): 548-560.
19. Abbasi, A.; Firouzi, B.; Sendur, P. Identification of unbalance characteristics of rotating machinery using a novel optimization-based methodology. Soft Computing: A fusion of foundations, methodologies and applications. 2022, 26:4831-4862.
20. Gu, Q.; Tang, Y. Research on computer-aided dynamic balancing machine measurement and analysis system. Mechanical Science and Technology. 1992, 4: 24-27.
21. Cui, Y.; Deng, S.; Yang, H.; Zhang, W.; Niu, R. Effect of cage dynamic unbalance on the cage’s dynamic characteristics in high-speed cylindrical roller bearings. Industrial Lubrication and Tribology. 2019, 71(10), 1125-1135.
22. Cui, Y.; Deng, S.; Ni, Y.; Chen, G. Effect of roller dynamic unbalance on cage stress of high-speed cylindrical roller bearing. Industrial Lubrication and Tribology. 2018, 70(9), 1580-1589.
23. Sui, X.; Liu, C.; Li, J.; Xue, Y.; Yu, Y.; Cui, Y. Laser-based measurement for micro-unbalance of cylindrical rollers of the high-speed precision rolling bearings. Cluster Computing. 2019, 22:S9159–S9167.
24. Liu,; Liu, Y.; Chen, S. Hydrostatic gas lubrication, 1st ed.; Harbin Institute of Technology: Harbin, China,1990; pp. 51-121.
25. Chen, G.; Ge, Y.; Lu, Q.; Zhang, W.; Wang, S. Air film pressure field characteristics of aerostatic thrust bearing with orifice blockage. The International Journal of Advanced Manufacturing Technology. 2023, 124:4317-4328.
26. Liang, S.; Duan, M.; Zhang, Z. Development and Investigation of Non-Destructive Detection Drive Mechanism for Precision Type Cylindrical Roller Dynamic Unbalance. Applied Sciences. 2023, 13(24): 13266.
27. Venturini, S.; Cavallaro, S. P.; Vigliani, Experimental Techniques for Flywheel Energy Storage System Self-discharge Characterisation[C]//The International Conference of IFToMM ITALY. Cham: Springer Nature Switzerland. 2024, 183-191.
28. Jin, X.; Liu, Y. Numerical and Experimental Analysis for the Dynamics of Flawed–Machining Rod–Disk Rotor with Inner Misalignment. Machines. 2022, 10(5), 355.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The authors added some revisions to the new version, but they didn't consider all of my recommendations. 

1. The references in Chinese are useless since they cannot be read.

2. There is no proper method for validating the results. They only showed their measurements, but no alternative method ensures they are correct.

 

Author Response

Point 1: The references in Chinese are useless since they cannot be read.

Response 1: Thank you very much for your comment, I have found as many relevant English references as possible, please check them out.

1. He, C.; Zhang, J.; Geng, K.; Wang, S.; Luo, M.; Zhang, X.; Ren, C. Advances in ultra-precision machining of bearing rolling elements. The International journal of advanced manufacturing technology. 2022, 122:3493-3524.
2. Xu, F.; Ding, N.; Li, N.; Liu, L.; Hou, N.; Xu, N.; Chen, X. A review of bearing failure Modes, mechanisms and causes. Engineering Failure Analysis. 2023,
3. Li, X.; Horie, M.; Kagawa, T. Study on the basic characteristics of a vortex bearing element. The International Journal of Advanced Manufacturing Technology. 2013, 64:1-12.
4. Wang, D.; Yuan, J.; Hu, L.; Lyu, B. Multidimensional study on the wear of high-speed, high-temperature, heavy-load bearings. Materials. 2023, 16(7), 2714.
5. Hou, X.; Diao, Q.; Liu, Y.; Liu, C.; Zhang, Z.; Tao, C. Failure Analysis of a Cylindrical Roller Bearing Caused by Excessive Tightening Axial Force. Machines. 2022, 10(5), 322.
6. Cui, Y.; Deng, S.; Niu, R.; Chen, G. Vibration effect analysis of roller dynamic unbalance on the cage of high-speed cylindrical roller bearing. Journal of Sound and Vibration. 2018, 434: 314-335.
7. Tiwari, R.; Chakravarthy, V. Simultaneous estimation of the residual unbalance and bearing dynamic parameters from the experimental data in a rotor-bearing system. Mechanism and Machine Theory. 2009, 44(4), 792-812.
8. Harsha, S. P. Nonlinear dynamic analysis of an unbalanced rotor supported by roller bearing. Chaos, Solitons & Fractals. 2005, 26(1), 47-66.
9. Wang, A.; Yao, W. Theoretical and numerical studies on simultaneous identification of rotor unbalance and sixteen dynamic coefficients of two bearings considering unbalance responses. International Journal of Control, Automation and Systems. 2022, 20(6), 1971-2007.
10. Therale, L. Dynamic balancing of rotating machinery in the field. ASME Journal of Applied Mechanics. 1934, 56: 745-753.
11. Baker, G. Methods of rotor-unbalance determination. ASME Journal of Applied Mechanics. 1939, 61: A1-A6.
12. Zhang, X.; Jiao, H.; Hu, D.; Research progress on field dynamic balancing methods for rotating machinery. Journal of Mechanical and Electrical Engineering. 2021, 38(11): 1367-1377 (in Chinese).
13. Zhang, L.; Duan, Z.; Li, D. Research progress of on-site dynamic balancing technology. Chemical Engineering and Machinery. 2012, 39(06): 690-694 (in Chinese).
14. Louis, Two-plane balancing of a rotor system without phase response measurements. Transactions of the ASME, Journal of Vibration, Acoustics, Stress,and Reliability in Design. 1987, 109(2): 162-167.
15. Bishop, E. D.; Gladwell, G. M. L. The Vibration and Balancing of an Unbalanced Flexible Rotor. Journal of mechanical Engineering science. 1959, 1(1): 66-70.
16. Zou, D.; Zhao, H.; Liu, G. Application of augmented Kalman filter to identify unbalance load of rotor-bearing system: Theory and experiment. Journal of Sound and Vibration. 2019, 463: 68-69.
17. Parkinson, G. Balancing of rotating machinery. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. 1991, 205(1): 61-63.
18. Kellenberger, Should a flexible rotor be balanced in N or (N+2) planes. Journal of Engineering for Industry. 1972, 94(2): 548-560.
19. Abbasi, A.; Firouzi, B.; Sendur, P. Identification of unbalance characteristics of rotating machinery using a novel optimization-based methodology. Soft Computing: A fusion of foundations, methodologies and applications. 2022, 26:4831-4862.
20. Gu, Q.; Tang, Y. Research on computer-aided dynamic balancing machine measurement and analysis system. Mechanical Science and Technology. 1992, 4: 24-27.
21. Cui, Y.; Deng, S.; Yang, H.; Zhang, W.; Niu, R. Effect of cage dynamic unbalance on the cage’s dynamic characteristics in high-speed cylindrical roller bearings. Industrial Lubrication and Tribology. 2019, 71(10), 1125-1135.
22. Cui, Y.; Deng, S.; Ni, Y.; Chen, G. Effect of roller dynamic unbalance on cage stress of high-speed cylindrical roller bearing. Industrial Lubrication and Tribology. 2018, 70(9), 1580-1589.
23. Sui, X.; Liu, C.; Li, J.; Xue, Y.; Yu, Y.; Cui, Y. Laser-based measurement for micro-unbalance of cylindrical rollers of the high-speed precision rolling bearings. Cluster Computing. 2019, 22:S9159–S9167.
24. Liu,; Liu, Y.; Chen, S. Hydrostatic gas lubrication, 1st ed.; Harbin Institute of Technology: Harbin, China,1990; pp. 51-121.
25. Chen, G.; Ge, Y.; Lu, Q.; Zhang, W.; Wang, S. Air film pressure field characteristics of aerostatic thrust bearing with orifice blockage. The International Journal of Advanced Manufacturing Technology. 2023, 124:4317-4328.
26. Liang, S.; Duan, M.; Zhang, Z. Development and Investigation of Non-Destructive Detection Drive Mechanism for Precision Type Cylindrical Roller Dynamic Unbalance. Applied Sciences. 2023, 13(24): 13266.
27. Venturini, S.; Cavallaro, S. P.; Vigliani, Experimental Techniques for Flywheel Energy Storage System Self-discharge Characterisation[C]//The International Conference of IFToMM ITALY. Cham: Springer Nature Switzerland. 2024, 183-191.
28. Jin, X.; Liu, Y. Numerical and Experimental Analysis for the Dynamics of Flawed–Machining Rod–Disk Rotor with Inner Misalignment. Machines. 2022, 10(5), 355.

 

 

Point 2: There is no proper method for validating the results. They only showed their measurements, but no alternative method ensures they are correct.

Response 2: Thank you very much for your comment. There are no proven products on the market that are comparable to our proposed test device, so we are unable to verify the validity of the results through comparative testing. When preparing the cylindrical roller test specimen, we use the de-weighting method to assign a series of known dynamic unbalance to the cylindrical roller, and then test to detect the amplitude value corresponding to the dynamic unbalance, and then back-calculate the value to obtain the dynamic unbalance of the cylindrical roller. Comparison of the two sets of dynamic unbalance values verifies the correctness of the device proposed in this paper.

 

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The changes I suggested have been implemented.

Author Response

Response: Thank you very much for your comments, your input has allowed us to correct many errors, I wish you good health and success in your endeavours..

Author Response File: Author Response.pdf