Research on Meshing Characteristics of Trochoidal Roller Pinion Rack Transmission

Round 1

Reviewer 1 Report

This paper focuses on a transmission mechanism and the trochoidal roller pinion rack. Paper is well written and formulated clearly but technically it needs some major revisions.

Abstract:

Follow the basic pattern of template of abstract formation….as:

We strongly encourage authors to use the following style of structured abstracts, but without headings: (1) Background: Place the question addressed in a broad context and highlight the purpose of the study; (2) Methods: Describe briefly the main methods or treatments applied; (3) Results: Summarize the article's main findings; and (4) Conclusions: Indicate the main conclusions or interpretations. (5) Add something about the benefits results of the research.  ……also give quantitative results in the abstract. 

[Please revise-according to point 2,3,4 and 5 Conclusion and benefits]

Introduction:

-Can you please establish the research gap [Please add]

-Please add a data table along with citation in the manuscript considering following points:

(a) Previously used material/leaves of other trees for same purpose (b) New material/leaves of other trees for same purpose to be studied (c) Previously asked Questions (d) Previously used techniques for similar type of research.

-Establish your research questions in this section.

-Update your literature review with more additional references of published work in recent years.

-So, establish a research gap and connect your research methodology, data analysis, results with that research gap and produce a discussion on future directions.

Materials and Methods

-A Comprehensive research framework is missing (flowchart). This portion should be written in step wise pattern so that readers can understand the procedure for implementation purpose. [Please add]

-Also add references(citations) related to applied methodology.

Limitations of the study:

-Please add heading about the limitations of the study.

-Suggestion/recommendation to the policy makers must be there and it is responsibility of scientist to device such solution which are practically applicable. 

 

Author Response

Point 1: Abstract:

Follow the basic pattern of template of abstract formation….as:

We strongly encourage authors to use the following style of structured abstracts, but without headings: (1) Background: Place the question addressed in a broad context and highlight the purpose of the study; (2) Methods: Describe briefly the main methods or treatments applied; (3) Results: Summarize the article's main findings; and (4) Conclusions: Indicate the main conclusions or interpretations. (5) Add something about the benefits results of the research.  ……also give quantitative results in the abstract.

[Please revise-according to point 2,3,4 and 5 Conclusion and benefits] 

 

Response 1:

We have completely revised the abstract according to the format requested by the reviewer. The revised abstract is showed as following:

Abstract: As a precision transmission mechanism, the trochoidal roller pinion rack has been paid more and more attention in recent years, but its meshing characteristics have not been deeply explored. In order to investigate the meshing characteristics of the trochoidal roller pinion rack transmission, it is particularly important to research its line of action and meshing stiffness. The equation of the line of action of the trochoidal roller pinion rack is deduced by using its tooth profile formation principle. The motion simulation of the trochoidal roller pinion rack transmission is carried out to verify the correctness of the theoretical derivation of the equation of the line of action, and the influence of the basic parameters on the line of action is summarized. The meshing stiffness of the trochoidal roller pinion rack is calculated based on the energy method used for gear meshing stiffness, and the meshing stiffness is defined considering the time-varying characteristics of its pressure angle, and the influence of each basic parameter on the meshing stiffness is studied. The results shows that the meshing stiffness increases first and then decreases in the double tooth meshing zone, while  the meshing stiffness gradually decreases in the single tooth meshing zone. The basic parameters including number of roller pins, the module, the rack tooth profile offset coefficient, the diameter coefficient of roller pins, and the addendum coefficient of rack have different effects on the line of action and meshing stiffness. The research conclusion can provide reference for the parameter design of the trochoidal roller pinion rack, and provide the meshing stiffness calculation method for the dynamic analysis of the transmission.

 

Point 2: Introduction:

-Can you please establish the research gap [Please add]

-Please add a data table along with citation in the manuscript considering following points: (a) Previously used material/leaves of other trees for same purpose (b) New material/leaves of other trees for same purpose to be studied (c) Previously asked Questions (d) Previously used techniques for similar type of research.

-Establish your research questions in this section.

-Update your literature review with more additional references of published work in recent years.

-So, establish a research gap and connect your research methodology, data analysis, results with that research gap and produce a discussion on future directions.

 

Response 2: 

The research of the equation of the line of action and computation of meshing stiffness for the trochoidal roller pinion rack has not been reported in the existing literatures. So these isuues are research gap of the trochoidal roller pinion rack. We added the description in the manuscript as following:

This paper innovatively deduces the equation of the line of action of the trochoidal roller pinion rack and studies its variation law, and then innovatively uses the energy method to calculate the meshing stiffness of the trochoidal roller pinion rack and study its variation law.

 

We added literature review with more additional references of published work in recent years as following:

[7] Zhang, Y.; Zhang, P.; Bao, B. Research of mechanical property of trochoid roller pinion rack transmissions. Journal of Mechanical Transmission, 2016, 40(6), 27- 31.

[10] Efremenkov, E. A.; Martyushev, N. V.; Skeeba, V. Y. Research on the possibility of lowering the manufacturing accuracy of cycloid transmission wheels with intermediate rolling elements and a free cage. Applied Sciences, 2022, 12, 5.

[11] Han, J.; Li, W.; Qiao, Z. Analysis of mixed lubrication characteristics of cycloid pin-wheel transmission. International Journal of Precision Engineering and Manufacturing, 2021, 22(3), 453-472.

[12] Li, T.; Tian, M.; Xu, H.; et al. Meshing contact analysis of cycloidal-pin gear in RV reducer considering the influence of manufacturing error. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2020, 42(3), 133.

[13] Yang, R.; Han, B.; Xiang, J. Nonlinear dynamic analysis of a trochoid cam gear with the tooth profile modification. International Journal of Precision Engineering and Manufacturing, 2020, 21(12), 2299-2321.

[14] Yang, R.; Han, Bo.; Li, F.; et al. Nonlinear dynamic analysis of a trochoid cam gear. Joural of Mechanical Design, 2020, 142(9), 094502.

[15] Xu, L.; Yang, Y. Dynamic modeling and contact analysis of a cycloid-pin gear mechanism with a turning arm cylindrical roller bearing. Mechanism and Machine Theory, 2016, 104(10), 327-349.

The related reviews of these literatures was added as following:

Zhang et al [6,7] deduced the theoretical tooth profile equation of the rack tooth profile based on the meshing principle of the trochoidal roller pinion rack mechanism, and studied meshing force and contact stress of trochoid roller pinion rack transmission.

Efremenkov [10] studied how to reduce the cost of manufacturing the parts for gears with intermediate rolling elements and, at the same time, maintain a high accuracy of the transmission mechanism. Han [11] presented a transient hybrid EHL model for cycloidal pinwheel transmission, which takes into account key variable parameters along the meshing surface, including contact load, curvature contact radius, and entrainment speed. Li [12] take the RV cycloidal-pin gear pair transmission as the object, a meshing contact analysis method is proposed for RV cycloidal-pin gear transmission considering the influence of manufacturing error. Yang [13,14] constructed the equations of tooth profile modification to analysis the nonlinear dynamics of the TCG. Xu [15] proposes a method for analyzing the contact dynamics of the multi-tooth meshing in a cycloidal-pin gear transmission was proposed considering the influences of the turning-arm cylindrical roller bearing.

 

Point 3: Materials and Methods:

-A Comprehensive research framework is missing (flowchart). This portion should be written in step wise pattern so that readers can understand the procedure for implementation purpose. [Please add]

-Also add references(citations) related to applied methodology.

 

Response 3:  

A comprehensive research flowchat has been added shown Figure 1.

 

Figure 1. The flowchart of research content

We added some references citations related to applied methodology, such as Equations (5), the material mechanics method [16], the conformal mapping method [17], the finite element method [18], the loaded tooth contact analysis method [19], the energy method [20], etc. The complete additions can be seen in the revised manuscript.

 

Point 4: Limitations of the study:

-Please add heading about the limitations of the study.

-Suggestion/recommendation to the policy makers must be there and it is responsibility of scientist to device such solution which are practically applicable.

 

Response 4: 

We added the heading of ‘7. Shortcomings and Prospects’ and some related discussions as following:

The derivation of the line of action equation of the trochoidal roller pinion rack in the article is a theoretical derivation based on the meshing principle. In this paper, only the simulation veri-fication is carried out, but the experimental verification is not carried out. The follow-up research can carry out experimental verification to further prove the derivation in this paper. In this paper, only the energy method is used for the theoretical calculation of meshing stiffness without veri-fication, and subsequent research can use other methods to calculate it and also carry out exper-imental verification.The research on the line of action equation in this paper can help to further understand the meshing principle and characteristics of the trochoidal roller pinion rack. The calculation of mesh stiffness can be used for subsequent trochoid roller rack dynamics studies.

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper is well structured and the methods are described in a scientific way. Therefore, the paper can be published after a minor revision:

• In the INTRODUCTION section, the literature review is not sufficient for a scientific article. you must review more articles in the same field, especially more articles from the MDPI journal.
• The last paragraph of the introduction shortly describes what you are going to investigate. However, the novelty of the paper is not clear. Please highlight your novelty.
• I cannot see the references related to your equations. All your equations must be cited.
• You used ADAMS for your simulations and you verified your data. How much is your uncertainty error? You must calculate the uncertainty analysis.

 

Author Response

Point 1: In the INTRODUCTION section, the literature review is not sufficient for a scientific article. you must review more articles in the same field, especially more articles from the MDPI journal. 

 

Response 1:

We added literature review with more additional references of published work in recent years as following:

[7] Zhang, Y.; Zhang, P.; Bao, B. Research of mechanical property of trochoid roller pinion rack transmissions. Journal of Mechanical Transmission, 2016, 40(6), 27- 31.

[10] Efremenkov, E. A.; Martyushev, N. V.; Skeeba, V. Y. Research on the possibility of lowering the manufacturing accuracy of cycloid transmission wheels with intermediate rolling elements and a free cage. Applied Sciences, 2022, 12, 5.

[11] Han, J.; Li, W.; Qiao, Z. Analysis of mixed lubrication characteristics of cycloid pin-wheel transmission. International Journal of Precision Engineering and Manufacturing, 2021, 22(3), 453-472.

[12] Li, T.; Tian, M.; Xu, H.; et al. Meshing contact analysis of cycloidal-pin gear in RV reducer considering the influence of manufacturing error. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2020, 42(3), 133.

[13] Yang, R.; Han, B.; Xiang, J. Nonlinear dynamic analysis of a trochoid cam gear with the tooth profile modification. International Journal of Precision Engineering and Manufacturing, 2020, 21(12), 2299-2321.

[14] Yang, R.; Han, Bo.; Li, F.; et al. Nonlinear dynamic analysis of a trochoid cam gear. Joural of Mechanical Design, 2020, 142(9), 094502.

[15] Xu, L.; Yang, Y. Dynamic modeling and contact analysis of a cycloid-pin gear mechanism with a turning arm cylindrical roller bearing. Mechanism and Machine Theory, 2016, 104(10), 327-349.

The related reviews of these literatures was added as following:

Zhang et al [6,7] deduced the theoretical tooth profile equation of the rack tooth profile based on the meshing principle of the trochoidal roller pinion rack mechanism, and studied meshing force and contact stress of trochoid roller pinion rack transmission.

Efremenkov [10] studied how to reduce the cost of manufacturing the parts for gears with intermediate rolling elements and, at the same time, maintain a high accuracy of the transmission mechanism. Han [11] presented a transient hybrid EHL model for cycloidal pinwheel transmission, which takes into account key variable parameters along the meshing surface, including contact load, curvature contact radius, and entrainment speed. Li [12] take the RV cycloidal-pin gear pair transmission as the object, a meshing contact analysis method is proposed for RV cycloidal-pin gear transmission considering the influence of manufacturing error. Yang [13,14] constructed the equations of tooth profile modification to analysis the nonlinear dynamics of the TCG. Xu [15] proposes a method for analyzing the contact dynamics of the multi-tooth meshing in a cycloidal-pin gear transmission was proposed considering the influences of the turning-arm cylindrical roller bearing.

 

Point 2: The last paragraph of the introduction shortly describes what you are going to investigate. However, the novelty of the paper is not clear. Please highlight your novelty.

 

Response 2: 

The research of the equation of the line of action and computation of meshing stiffness for the trochoidal roller pinion rack has not been reported in the existing literatures. So these isuues are research gap of the trochoidal roller pinion rack. We added the description in the manuscript as following:

This paper innovatively deduces the equation of the line of action of the trochoidal roller pinion rack and studies its variation law, and then innovatively uses the energy method to calculate the meshing stiffness of the trochoidal roller pinion rack and study its variation law.

 

Point 3: I cannot see the references related to your equations. All your equations must be cited.

 

Response 3: 

Formulas 5 and 20 are cited from reference [6], formulas 9~11, and 13~19 are cited from literature [21], and the related references have been cited for these equations. The rest of the formulas are derived from the paper.

 

Point 4: You used ADAMS for your simulations and you verified your data. How much is your uncertainty error? You must calculate the uncertainty analysis.

 

Response 4: 

The uncertainty analysis of simulation values was carried out by using the calculated variance values. The detailed data was added to table 3. The relevant description is as follows:

According to the variance calculation method, the rack simulation uncertainty is 0.0189 and the roller simulation uncertainty is 0.0172.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The article has undergone significant changes. However, the authors seem upset that we, the reviewers, want to correct the materials in order to publish scientific quality articles. After re-evaluating the material, I consider that the content should be rearranged and rewritten accordingly. Unfortunately, it has now become a conglomerate of information without sufficient scientific support.

Author Response

According to expert comments, we revised the manuscript throughout. The layout and sentences have been comprehensively improved. Please see the revised manuscript for details. Meanwhile, some major additions and modifications are as followings.

 

So far, the research on trochoidal roller pinion rack is still at the stage of basic principle, and further research on it is of great significance to its development. Further research is of great significance to its development. Section 3 of this paper deduces its equation of the line of action based on the meshing principle of trochoidal roller pinion rack. Since this equation is deduced for the first time, the simulation method is used to verify its correctness in Section 4. Section 5 uses the energy method used for gear mesh stiffness to calculate the mesh stiffness of the trochoidal roller pinion rack. This mesh stiffness calculation is only used as a reference for the follow-up research, and its verification will be carried out in the follow-up research.

 

Reference [6] has carried out a detailed study of the trochoid rack tooth profile, and its meshing principle and tooth profile equation have been studied. This paper further studies the line of action of the trochoid roller pinion rack on the basis of reference [6]. The meshing principle is used to deduce the equation of the line of action, but since no scholars have studied the line of action of the trochoid roller pinion rack before, in order to prove the correctness of the derivation of the equation of the line of action in this paper, in Section 4 of this paper, kinematics simulation of the trochoid roller pinion rack is carried out to prove the correctness of the theoretical derivation.

 

The research on meshing stiffness plays an important role in dynamics research. As a new type of precision machinery, the meshing stiffness of the trochoid roller pinion rack are still blank. In this section, the meshing stiffness of the trochoid roller pinion rack is theoretically calculated with reference to the energy method used for the calculation of gear meshing stiffness. Since the teeth of the gear and the teeth of the trochoid rack have similar characteristics, this paper uses the energy method in reference [21] to replace the gear model with the rack model to calculate its meshing stiffness. This paper only proposes its meshing stiffness calculation method as a reference for follow-up research, its experimental verification will continue in follow-up research.

Author Response File: Author Response.docx