Study on Dynamics of a Two-Stage Gear Transmission System with and without Tooth Breakage

Round 1

Reviewer 1 Report

The present article describes a simple torsional model for gear dynamics considering a time varying mesh stiffness and backlash functions including tooth breakage as well. The time varying mesh stiffness is simplified as a sinusoidal function with the mean value computed from a questionable FE model, which is too simple to be considered of any accuracy. Some results are presented, but very few actual insights are presented. The main findings are that when tooth breakage is introduced the motion becomes more chaotic and amplitudes increase, which is to be expected. An experimental setup is also presented, but the correlation with the proposed model is not clear. 

In the reviewer opinion a major revision is required. Some improvements can be:
1) Considering the excitation as a sinusoidal function is too simplistic. At least introduce further harmonics coming from the Static Transmission Error in the calculation
2) A FE model of that kind is unsuitable to understand the actual stiffness of the engagement. Introduce the actual geometry of the gear and the engaged driven gear with contact analysis to obtain correct displacements.
3) Improve the correlation with the experimental results. It is very difficult right now to obtain any meaning from the current presentation.
4) Improve quality and text size of the figures.

Author Response

Thanks very much for taking your time to review this manuscript. I really appreciate all your comments and suggestions! Please find my itemized responses in below and my revisions/corrections in the re-submitted files.

Comments and Suggestions for Authors

The present article describes a simple torsional model for gear dynamics considering a time varying mesh stiffness and backlash functions including tooth breakage as well. The time varying mesh stiffness is simplified as a sinusoidal function with the mean value computed from a questionable FE model, which is too simple to be considered of any accuracy. Some results are presented, but very few actual insights are presented. The main findings are that when tooth breakage is introduced the motion becomes more chaotic and amplitudes increase, which is to be expected. An experimental setup is also presented, but the correlation with the proposed model is not clear. 

In the reviewer opinion a major revision is required. Some improvements can be:
1) Considering the excitation as a sinusoidal function is too simplistic. At least introduce further harmonics coming from the Static Transmission Error in the calculation

Thanks for your professional advice. Gear motion is a periodic motion. As a typical periodic function, the sine function can be more convenient to explore the law of excitation changes over time.The theoretical model of the gear transmission system in this paper is a simplified analysis model, which is more conducive to directly explaining the influence of the fault on the dynamic characteristics of the gear transmission system.

2) A FE model of that kind is unsuitable to understand the actual stiffness of the engagement. Introduce the actual geometry of the gear and the engaged driven gear with contact analysis to obtain correct displacements.

Thank you for your valuable advice.The meshing process of the gears is a process of mutual contact movement. One of the gears is simplified into an elastic cantilever beam, and the actual rigidity during the meshing process can also be achieved by setting an appropriate force to contact the cantilever beam.

3) Improve the correlation with the experimental results. It is very difficult right now to obtain any meaning from the current presentation.

Thank you for your constructive comments. I have reorganized the relationship between the results of the experimental part and the dynamic analysis of the gear transmission system.

4) Improve quality and text size of the figures.

Thanks for your observant comment. According to your suggestion, we must revise the text format again. Thanks again for your careful review.

Author Response File: Author Response.docx

Reviewer 2 Report

1) Significant number of transmissions, especially in the automotive, use helical gears. Please comment on the relevance of the presented study with respect to its application on helical gears.

2) The experimental setup includes the gearbox powered by an electrical motor without any load on the opposite side. It would be expected that the tooth breakage would occur when the gear is under noticeable load and that the problems in further operation would also be related dominantly to operation under load. Please comment. 

Author Response

Thanks very much for taking your time to review this manuscript. I really appreciate all your comments and suggestions! Please find my itemized responses in below and my revisions/corrections in the re-submitted files.

1) Significant number of transmissions, especially in the automotive, use helical gears. Please comment on the relevance of the presented study with respect to its application on helical gears.

The research object of this paper focused on the gears applied in the transmission system of wind turbine, hence the spur gear is mainly considered. Specifically, the vibration characteristics of the gear transmission system is studied to identify the faults in the gearbox, which is essential to ensure the stable operation of the gear transmission systemof wind turbine.

2) The experimental setup includes the gearbox powered by an electrical motor without any load on the opposite side. It would be expected that the tooth breakage would occur when the gear is under noticeable load and that the problems in further operation would also be related dominantly to operation under load. Please comment. 

The load end of this experimental device is equipped with magnetic powder brake,it can generate load by adjusting excitation current.

Thank you!!!

 

Author Response File: Author Response.docx

Reviewer 3 Report

The diagnosis of the gearbox is of interest to engineers and researchers from various fields of the industry. Taking into account that the spectrum of acquired vibration signal generated in the gearing process always contains the gear-mesh frequency (GMF), and many other frequencies (e.g., the hunting frequency), gears diagnosis is more difficult to realize than rolling bearings' diagnosis (where the spectrum of a normal functioning does not present any signatures, except the spindle rotational frequency). From this point of view, there is enough room for novel research in the gearbox diagnosis, any new result being welcome. 

Personally, after I carefully read the paper, I consider that the authors proposed a concept of gearbox diagnosis, the dynamic theoretical model being validated with experimental results.  Anyway, I have some suggestions that may improve the quality and the clarity of  the current paper:

1. The Introduction section is too large for an article, but it can be left like this. The weak point of the Introduction is the fact that the authors did not clearly state the originality of their paper. Is the proposed model original and novel?! The experimental section is very poor in results, just one validation. What this paper brings new to the knowledge in gearbox diagnosis?
2. In Figure 15, the parts of the test rig are neither specified, nor mentioned in the text. Information on used sensor type and characteristics, data acquisition board, and the emplacement of the sensor must be provided.
3. At lines 382-383, why wavelet reduction algorithm was applied to the acquired signals, and how? The theoretical study was using only FFT.  The wavelet algorithm must be presented, or references must be cited. 
4. Line 309: what scheme are the authors talking about?! There is no scheme presented in Figure 9.
5. What is the chaotic state of the gears, and how did the authors model it?
6. Specify the units for the Von Mises stress in Figure 4, and comment on the results.
7. Lines 396-397: the gear mesh frequency characterizes the entire gear process and not just the pinion. Besides the GMF, gear and pinion rotational frequencies,  the hunting tooth frequency (HTF), assembly phase-frequency (AFF), gear natural frequencies (GNF), and the ghost or phantom frequencies (GPF) should be at least theoretically computed and identified where possible on the real spectrum of the gearbox. 
8. The discussions on the results presented in Figure 17 should mention that the amplitude of the GMF increased in the case of a broken tooth. The broken tooth was missing from pinion or from gear?

Author Response

Thanks very much for taking your time to review this manuscript. I really appreciate all your comments and suggestions! Please find my itemized responses in below and my revisions/corrections in the re-submitted files.

The diagnosis of the gearbox is of interest to engineers and researchers from various fields of the industry. Taking into account that the spectrum of acquired vibration signal generated in the gearing process always contains the gear-mesh frequency (GMF), and many other frequencies (e.g., the hunting frequency), gears diagnosis is more difficult to realize than rolling bearings' diagnosis (where the spectrum of a normal functioning does not present any signatures, except the spindle rotational frequency). From this point of view, there is enough room for novel research in the gearbox diagnosis, any new result being welcome. 

Personally, after I carefully read the paper, I consider that the authors proposed a concept of gearbox diagnosis, the dynamic theoretical model being validated with experimental results.  Anyway, I have some suggestions that may improve the quality and the clarity of  the current paper:

1. The Introduction section is too large for an article, but it can be left like this. The weak point of the Introduction is the fact that the authors did not clearly state the originality of their paper. Is the proposed model original and novel?! The experimental section is very poor in results, just one validation. What this paper brings new to the knowledge in gearbox diagnosis?

Thanks for the suggestion of the reviewer, the authors have compressed the introduction.

The model isproposed based on previous studies, the model cited in this paper analyzes the dynamic characteristics of the gear transmission system in the normal state and the fault state during the periodic motion and the chaotic motion. The analysis shows that the fault is easier to identify under the periodic motion state. Due to the limited experimental conditions, only one verification has been done at present, and a variety of failure research and verification will be carried out in the future work.

2. In Figure 15, the parts of the test rig are neither specified, nor mentioned in the text. Information on used sensor type and characteristics, data acquisition board, and the emplacement of the sensor must be provided.

Thanks for the reviewer’s suggestion. The authors have added the following description in the revised manuscript.

“During the experimental test,the YA series of three-directional accelerometer was selected, which can collect vibration signals in X, Y, and Z directions. The advantage of this sensor is that it has a wide range of installation positions and strong flexibility. In this paper, the YSV8016 dynamic signal acquisition instrument was used to convert the analog signal into digital signal, and then the computer will record the digital signal to complete the acquisition of the vibration signal. The gearbox bearing seat was selected as the measuring position.”

3. At lines 382-383, why wavelet reduction algorithm was applied to the acquired signals, and how? The theoretical study was using only FFT.  The wavelet algorithm must be presented, or references must be cited. 

Thanks for the suggestion of the reviewer, the authors haveciteda related reference [44] to explain the wavelet algorithm.

4. Line 309: what scheme are the authors talking about?! There is no scheme presented in Figure 9.

Figure 9 discusses the frequency domain analysisof the gear transmission system under its normal condition with .

5. What is the chaotic state of the gears, and how did the authors model it?

Chaos refers to the unpredictable, random-like motion that a deterministic dynamic system is sensitive to initial values, and is an inherent property. Chaos is obtained due to the introduced nonlinear factors in the dynamic model, such as time-varying meshing stiffness, comprehensive meshing error, and tooth flank clearance.

In order to distinguish chaos from periodic motion, the phase portrait and Poincaré mapare observed.If the vibration is periodic, itstrajectory in phase portrait will form a completed cycleafter the corresponding excitation periods, and its Poincaré map will show the determined number of points. However, when the vibration is chaotic,no matter how many excitationperiodshave beenexperienced,itsvibration can notgo back to the initialtrajectory, and its Poincaré map will show groups of points gathered together.

6. Specify the units for the Von Mises stress in Figure 4, and comment on the results.

Thanks for the reviewer’s reminding, the unit for the Von Mises stress has been added in the caption. The Von Mises stress cloud diagram is plotted for the calculation of the stiffness of single tooth.

7. Lines 396-397: the gear mesh frequency characterizes the entire gear process and not just the pinion. Besides the GMF, gear and pinion rotational frequencies,  the hunting tooth frequency (HTF), assembly phase-frequency (AFF), gear natural frequencies (GNF), and the ghost or phantom frequencies (GPF) should be at least theoretically computed and identified where possible on the real spectrum of the gearbox. 

Thanks for the reviewer’s reminding. In this present work, the authors only focused on the most basic dynamic characteristics of a two-stagegear transmission system, and to find a way to check the tooth breakage. Therefore, the other influence factors were not taken into consideration, and the authors will do that in the following research.

8. The discussions on the results presented in Figure 17 should mention that the amplitude of the GMF increased in the case of a broken tooth. The broken tooth was missing from pinion or from gear?

Thanks for the reviewer’s suggestion. The authors have added the following description in the revised manuscript.

“Numerical simulation shows that the amplitude of the dominantfrequency in the fault state (shown in Figure 17 (a)) is higher than that in the normal state (shown in Figure 16 (a)). Furthermore, comparing Figure 17 (b) with Figure 16 (b), the experimental results also show the same result. Therefore,it can be concluded that the amplitude of the dominantfrequency increases when the tooth of gear breaks.”

The medium-speed pinion gear was replacedbya gear with tooth breakage as shown in Fig. 2, and then the experimental test was carried out.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Quality of the figures has not been improved at all. 

Figure 1 is blurry, as well as the other results.

Author Response

Thanks very much for taking your time to review this manuscript. I really appreciate all your comments and suggestions! Please find my itemized responses in below and my revisions/corrections in the re-submitted files.

Comment:

Quality of the figures has not been improved at all.

Figure 1 is blurry, as well as the other results.

Response:

Thanks again for your careful reading of our revised manuscript; we have proofread the whole manuscript again. Meanwhile, in order to further improve the resolutions of figures displayed in this manuscript, we redrew Figure 1, and increased the sizes of points plotted in both Figures 5 and 6. We also adjusted the alignment of the equations.

Author Response File: Author Response.docx

Reviewer 2 Report

Some editing is required - the equations are not correctly aligned and the resolution of figures should be increased.

Author Response

Thanks very much for taking your time to review this manuscript. I really appreciate all your comments and suggestions! Please find my itemized responses in below and my revisions/corrections in the re-submitted files.

Comment:

Some editing is required - the equations are not correctly aligned and the resolution of figures should be increased.

Response:

Thanks again for your careful reading of our revised manuscript; we have proofread the whole manuscript again. Meanwhile, in order to further improve the resolutions of figures displayed in this manuscript, we redrew Figure 1, and increased the sizes of points plotted in both Figures 5 and 6. We also adjusted the alignment of the equations.

Author Response File: Author Response.docx

Reviewer 3 Report

The authors responded to all the questions and amended the paper as suggested. I recommend this paper for publication.

 

Author Response

Thanks very much for taking your time to review this manuscript. I really appreciate all your comments and suggestions! Please find my itemized responses in below and my revisions/corrections in the re-submitted files.

The authors responded to all the questions and amended the paper as suggested. I recommend this paper for publication.

Many thanks for your productive work, and much appreciated!

Author Response File: Author Response.docx