Research on the Principle and Suppression Method of Micro-Vibration Generation in a Spatial Optoelectronic Mechanism
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsEq. (16) is incorrect and should be improve. The rest of manuscript looks good.
Comments on the Quality of English LanguageIt seems that minor editing of English language is required.
Author Response
Comment 1：Eq. (16) is incorrect and should be improve. The rest of manuscript looks good.
Response 1：Thank you for pointing this out .I agree with this comment.
Equation 16 is incorrect and has been modified to the correct one ,the text has also been updated accordingly.
Comment 2：It seems that minor editing of English language is required.
Response 2：The English spelling and editing in the paper has been revised.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsIn the paper the micro vibration generation in a spatial optoelectronic mechanism is considered. The effect of mesh in the worm and worm gear is considered. The simulation of the system is done and the obtained results are compared with experimental ones.
Comments on the paper are as follows:
1. In the Introduction the titles of the authors of papers have to be deleted.
2. In the Sec.3 the mathematical model of the system is introduced. The system contains 8 differential equations of motions: 2 coupled and 6 uncoupled ones. Please explain, how do you obtain these equations? If the already published model is presented, please give the reference! Otherwise, the list of symbols is missing, It is necessary to be added.
3. The notation in the text and in Fig.5 is different. Why? Check.
4. Are the angles in equations (1)-(8) constant or time variable?
5. The effect of mesh between worm and worm gear is necessary to be included into the model. How can it be considered separately of model?
6. It is stated: M (t) is a non-linear change over time. Please, specify. Is it a periodical time function?
7. In 3.2.1 the differential equation for rotation of a body along an unmovable axis is presented. The relation is well known and has nothing to do with the paper! In addition, the equation (16) is not correct!
8. In 3.3 it is mentioned: The model is first simplified. What it means for equations (1)-(8)? What simplification is done in these equations which are necessary for simulation?
9. The simplified model mainly consists of worm gear, worm gear, worm gear
mounting bracket, and base. Explain!
The paper need major revision.
Author Response
Thank you for your review comments.
Comment 1：In the Introduction the titles of the authors of articals have to be deleted.
Response 1：Thank you for pointing this out .I agree with this comment.Two instances of Professor appear in the Introduction, both of which have been deleted.
Comment 2：In the Sec.3 the mathematical model of the system is introduced. The system contains 8 differential equations of motions: 2 coupled and 6 uncoupled ones. Please explain, how do you obtain these equations? If the already published model is presented, please give the reference! Otherwise, the list of symbols is missing, It is necessary to be added.
Response 2：Thank you for pointing this out .I agree with this comment.These 8 kinematic formulas are derived from the cited literature “Dynamics study and diagnosis with vibration analysis from worm gear manufactured by reverse engineering techniques》”. In this reference, the kinematic model of the worm gear is modeled and the force situation of the two during motion is analyzed. When conducting micro vibration analysis, this artical cites this modeling and force situation analysis.
Regarding this reference, citation 26 has been added to the artical.
Comment 3：The notation in the text and in Fig.5 is different. Why? Check.
Response 3：Thank you for pointing this out .I agree with this comment.This is a marking error. The correct one is Figure 6, which has been corrected in the text.
Comment4：Are the angles in equations (1)-(8) constant or time variable?
Response 4： are constants, they are inherent properties of worm gear and worm ， Different angles represent different worm gear structures.
But the θ angle is a parameter related to time. This artical studies that different external winding torques will bring different angular accelerationsß , resulting in different angles θ. The winding torque is time-dependent, so the θ angle is also time-dependent and varies.
Comment5：The effect of mesh between worm and worm gear is necessary to be included into the model. How can it be considered separately of model?
Response 5：The meshing clearance of the worm gear is necessary, but the requirements for clearance vary for different motion mechanisms; A meshing clearance that is too large can lead to greater backlash error, while a smaller meshing clearance can cause jamming.
In Chapter 3.2 of the artical, the characteristics of the motion mechanism mentioned in this artical are described. It is a meshing mechanism with a certain meshing clearance, and the worm gear is affected by external wire winding torque during the motion process. Moreover, the external cable torque changes irregularly.
In this artical, the force analysis of the motion process of the worm gear is carried out, and the meshing clearance is θ. Due to the generation of this clearance, when the worm gear has a driving force, it will accelerate towards the worm gear, causing impact. According to formula 15-21, the magnitude of the impact force energy is positively correlated with the meshing clearance and external driving force.
In sections 3.2.1-3.2.4 of the artical, various stress conditions of the worm gear are analyzed, and it is concluded that the fundamental cause of micro vibration is the existence of meshing clearance, and the induced cause is external wire winding torque.
Comment 6：It is stated: M (t) is a non-linear change over time. Please, specify. Is it a periodical time function?
Response 6：M (t) refers to the winding torque during cable operation, which is not a periodic function and may vary under different environmental conditions; For example, in the ground environment, under the influence of gravity, it is a kind of wire winding torque during operation. However, when in space, due to weightlessness or changes in space temperature, the cable will become harder or softer accordingly, and M (t) will be a different parameter.
Comment 7：In 3.2.1 the differential equation for rotation of a body along an unmovable axis is presented. The relation is well known and has nothing to do with the artical! In addition, the equation (16) is not correct!
Response 7：Thank you for pointing this out .The differential equations mentioned in section 3.2.1 are relevant to this artical. Sections 3.2.1-3.2.4 in the artical analyze four types of forces acting on the worm gear. Due to the presence of clearance and external winding torque, the winding torque has different directions. Sometimes the winding torque promotes the worm to collide with the worm gear, and sometimes hinders its impact. Different impact situations represent different impact energies, which in turn represent different micro vibration situations. Therefore, the differential equations mentioned in this artical are a physical and mathematical analysis of the micro impact process.
Equation 16 is incorrect and has been modified to the correct one and the text has also been updated accordingly.
Comment 8：In 3.3 it is mentioned: The model is first simplified. What it means for equations (1)-(8)? What simplification is done in these equations which are necessary for simulation?
Response 8：Thank you for pointing this out .The original model consists of a worm gear, worm, worm end angular contact bearing and its fixed bracket, worm gear fixed bracket, worm gear end angular contact bearing and other parts. In this artical, the model is simplified, leaving only the worm gear and worm . At the same time, the installation bracket of the worm gear is simplified as a straight rod, connected to the installation bottom surface, and measuring points are set on the installation bottom surface.
In the simulation model, the central axis of the worm wheel is subjected to concentric rotation constraints, simulating the effect of the angular contact bearing at the worm end, and applying drive to the worm end to simulate the impact force of the worm on the installation bottom surface under different meshing clearances; Fix the meshing clearances and apply a wire winding torque in the same or opposite direction to the worm end drive on the worm gear. Observe the impact force of the worm gear on the installation bottom surface at this time;
Through the above simulation analysis, it can be found that the meshing clearance of the worm gear and the external interference torque do indeed have a micro vibration effect on the installation bottom surface.
Equations (1) - (8) are not relevant to the simulation analysis here, which is related to the formulas in section 3.2.1.
Comment 9:The simplified model mainly consists of worm gear, worm gear, worm gear mounting bracket, and base. Explain!
Response 9:Thank you for pointing this out .The original model consists of a worm gear, worm, worm end angular contact bearing and its fixed bracket, worm gear fixed bracket, worm gear end angular contact bearing and other parts. In this artical, the model is simplified, leaving only the worm gear and worm . At the same time, the installation bracket of the worm gear is simplified as a straight rod, connected to the installation bottom surface, and measuring points are set on the installation bottom surface.
In the simulation model, the central axis of the worm is subjected to concentric rotation constraints, simulating the effect of the angular contact bearing at the worm end, and applying drive to the worm end to simulate the impact force of the worm on the installation bottom surface under different meshing clearances; Fix the meshing clearances and apply a wire winding torque in the same or opposite direction to the worm end drive on the worm gear. Observe the impact force of the worm gear on the installation bottom surface at this time.
If the model is not simplified, it is not conducive to simulation analysis. At the same time, after simplifying the model, applying corresponding constraints will not affect the consistency between the simulation results and the actual situation. Therefore, the above simplification is carried out.
The revised full text has been submitted, and the modified parts have been highlighted in red.
Thank you again for your review.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsAlthough the paper presents an interesting topic of mitigating the optical instrument vibrations originating from the positioning mechanism, we feel that the paper needs significant improvements, as follows. The authors indicate that the primary causes of the optical instrument vibrations are external excitation force and worm gear clearance. Furthermore, the authors demonstrate that the vibrations may be reduced by design changes. However, the process of arriving at such well-known conclusion is not addressed in the paper. How do the analytical and numerical analyses presented in Section 3 relate to the new design of the structure? How does the design change affect the mathematical models? Does the mathematical model (e.q. equations 1 - 14) indicate the design improvements? The measurements in Section 4 are presented as simple time-domain plots of the signals -- we feel that it would be insightful to present more detailed signal information (basic statistical characteristics, frequency content, etc.). Thus, we feel that the paper needs significant improvements before publishing.
Comments on the Quality of English LanguageThe sentence structure is sometimes very unclear. Several grammatical errors are present.
Author Response
Thank you for your review comments
Comment 1：Although the artical presents an interesting topic of mitigating the optical instrument vibrations originating from the positioning mechanism, we feel that the artical needs significant improvements, as follows.
The authors indicate that the primary causes of the optical instrument vibrations are external excitation force and worm gear clearance. Furthermore, the authors demonstrate that the vibrations may be reduced by design changes.
However, the process of arriving at such well-known conclusion is not addressed in the artical.
Response 1:Thank you for pointing this out .In Chapter 3.2 of this artical, the force analysis of the worm gear motion mechanism is carried out by analyzing the four motion states of the worm gear.
In the first motion state, the worm with a camera rotates from+90 ° to+XX ° (the position where the line winding torque is balanced, and from this stage to YY °, the line winding torque is very small or zero). During the process of rotating from+90 ° to+XX °, the force analysis of the worm gear is carried out, and it is found that due to the existence of the line winding torque, and the direction of the line winding torque is the same as the direction of the worm gear rotation, it promotes the operation of the worm gear. At this time, the meshing clearance between the worm and the worm gear teeth is the lower end meshing contact. When the worm gear rotates away from the contact surface of the worm gear, the meshing clearance between the worm and the worm gear will appear, and the line winding torque will carry the worm to collide with the worm gear; If there is no meshing clearance between the worm and the worm gear, there is no possibility of impact, but the key is that the meshing clearance must exist, which provides space for the worm to accelerate and cause impact vibration.
In the second motion state, the worm with a camera rotates from+XX ° (the position where the line winding torque is balanced, and the line winding torque will increase in the direction of+90 °) to+90 °. During this process, the force analysis of the worm is carried out, and it is found that due to the existence of the line winding torque, which is opposite to the direction of the worm rotation, the line winding torque will bring the worm into close contact with the worm gear. The worm pushes the worm gear in motion, and the micro vibration generated at this time is significantly smaller because the worm gear moves closely, which is equivalent to a small mesh clearance. At this time, the micro vibration is small.
By conducting force analysis on the third and fourth working conditions, it can be concluded that the main causes of micro vibrations are the clearance between the worm gear and the wire winding torque.
In Chapter 3.3, the kinematic simulation of the worm gear was carried out using ADAMS software. By setting different meshing clearances or external interference forces, the vibration of the bottom surface of the worm gear installation was measured. Through simulation analysis, it was verified that the meshing clearance of the worm gear and the influence of the winding torque were the main causes of micro vibration.
Comment 2：How do the analytical and numerical analyses presented in Section 3 relate to the new design of the structure?
Response 2:Thank you for pointing this out.The mathematical models 1-14 introduced in Chapter 3.1 mainly refer to the force analysis of worm and worm gear during the meshing process in reference (26), which is a universal force analysis for worm and worm gear motion mechanisms and can be applied to all worm and worm drive mechanisms.
The mathematical formulas 15-21 in Chapter 3.2 are mainly applicable to the two-dimensional pointing mechanism of the worm gear designed in this artical. Through the analysis of four different working conditions, it is found that the meshing clearance θ of the worm gear and the external winding torque M (t) are the key factors affecting micro vibration.
The clearance θ between the worm gear and worm gear is necessary, and in the later structural design, it can be controlled to be 0.03mm; The external winding torque M(t) can be significantly reduced through the new dual inner stator structure design, thus achieving the effect of reducing micro vibrations through the new structural design.
Comment 3：How does the design change affect the mathematical models?
Response 3:Thank you for pointing this out.The design improvement in this artical is mainly reflected in mathematical model 15-21. By optimizing the double inner stator design of the worm gear mechanism, the cable is designed to pass through the pitch axis and azimuth axis. During the operation of the pitch and azimuth axis systems, the cable passing through the axis will also have a certain interference force, but the force arm of this interference force is reduced to only the radius of the axis passing hole, so the wire winding torqueM(t) will be reduce exponentially. The reduction of the wire winding torque can be reflected in the mathematical model of 15-21. After the wire winding torque is reduced, the most direct impact force of the worm gear is reduced, thereby achieving the effect of reducing micro vibration.
Comment 4：Does the mathematical model (e.q. equations 1 - 14) indicate the design improvements?
Response 4:Thank you for pointing this out.Mathematical model 1-14 is the mathematical model of the motion of the worm gear mechanism, and the design improvement in this artical is mainly reflected in mathematical model 15-21. By optimizing the double inner stator design of the worm gear mechanism, the cable is designed to pass through the pitch axis and azimuth axis. During the operation of the pitch and azimuth axis systems, the cable passing through the axis will also have a certain interference force, but the force arm of this interference force is reduced to only the radius of the axis passing hole, so the wire winding torque will be reduce exponentially. The reduction of the wire winding torque can be reflected in the mathematical model of 15-21. After the wire winding torque is reduced, the most direct impact force of the worm gear is reduced, thereby achieving the effect of reducing micro vibration.
Comment 5：The measurements in Section 4 are presented as simple time-domain plots of the signals -- we feel that it would be insightful to present more detailed signal information (basic statistical characteristics, frequency content, etc.). Thus, we feel that the artical needs significant improvements before publishing.
Response 5:Thank you for pointing this out.The measurement results in Section 4 are derived from the micro vibration measurement platform mentioned in the artical. The upper computer software of the micro vibration testing platform can output data and graphs of the testing process. The horizontal axis of the data and graphs is time, and the vertical axis is the force or torque values in three directions. At the same time, the upper computer software will output an Excel table containing all the data on the graph. However, the time accuracy of the table is very high, as shown in the figure below, and it cannot be displayed in the artical. The test results can only be displayed by displaying the output graph.
Comment 6:The sentence structure is sometimes very unclear. Several grammatical errors are present.
Response 6:Thank you for pointing this out.I agree with the comment.The sentences in the paper have been streamlined, and relevant grammar errors have been corrected.
The revised full text has been submitted, and the modified parts have been highlighted in red.
Thank you again for your review.
Author Response File: Author Response.pdf
Reviewer 4 Report
Comments and Suggestions for AuthorsThe manuscript titled "Research on the Principle and Suppression Method of Micro Vibration Generation in a Spatial Optoelectronic Mechanism" presents a compelling analysis of the micro-vibration generation mechanisms in a space scanning system, with a particular focus on the worm gear and worm gear mechanisms. The study optimizes the design and provides experimental verification of the proposed solutions. The paper aligns well with the scope of Machines and requires only minor revisions before publication. Below are the comments:
Introduction: Please revise the sentence: "Professor Šmeringaiová studied a performance analysis method [1-4]. By building a worm gear and worm vibration testing platform, she was able to quickly analyze performance data." Correct the English and remove the title "Professor." Replace it with the first authors of the cited manuscripts. This issue recurs throughout the introduction, for example, with "Sushmita Kamble" in the following paragraph and other instances. Ensure adherence to international referencing standards, particularly the MDPI format.
Section 3.3: Include more details about the ADAMS simulations and provide appropriate references.
Section 4.3 (Experimental Summary): Please review and correct the punctuation in Table 1.
References: Incorporate more international sources, as many of the current references are centered on Chinese technology. Additionally, ensure consistency in formatting, as some references are in uppercase while others are not. If applicable, consider adding references from the Machines journal.
Comments on the Quality of English LanguageNo comments.
Author Response
Thank you for your review comments
Comment 1：Introduction: Please revise the sentence: "Professor Šmeringaiová studied a performance analysis method [1-4]. By building a worm gear and worm vibration testing platform, she was able to quickly analyze performance data." Correct the English and remove the title "Professor." Replace it with the first authors of the cited manuscripts. This issue recurs throughout the introduction, for example, with "Sushmita Kamble" in the following paragraph and other instances. Ensure adherence to international referencing standards, particularly the MDPI format.
Response 1:Thank you for pointing this out.I agree with this comment.The article has made modifications to this type of issue and removed title information such as Professor.
Comment 2:Section 3.3: Include more details about the ADAMS simulations and provide appropriate references.
Response 2:Thank you for pointing this out.I agree with this comment.In Chapter 3.3, the following content has been added regarding ADAMS kinematic simulation, along with references to ADAMS modeling and simulation (27-28).
The original model consists of a worm gear, worm, worm end angular contact bearing and its fixed bracket, worm gear fixed bracket, worm gear end angular contact bearing and other parts. In this artical, the model is simplified, leaving only the worm gear and worm . At the same time, the installation bracket of the worm gear is simplified as a straight rod, connected to the installation bottom surface, and measuring points are set on the installation bottom surface.
In the simulation model, the central axis of the worm is subjected to concentric rotation constraints, simulating the effect of the angular contact bearing at the worm end, and applying drive to the worm end to simulate the impact force of the worm on the installation bottom surface under different meshing clearances.
Comment 3:Section 4.3 (Experimental Summary): Please review and correct the punctuation in Table 1.
Response 3:Thank you for pointing this out.I agree with this comment.In Chapter 4.3, the punctuation marks in Table 1 have been changed.
Comment 4:References: Incorporate more international sources, as many of the current references are centered on Chinese technology. Additionally, ensure consistency in formatting, as some references are in uppercase while others are not. If applicable, consider adding references from the Machines journal.
Response 4:More international resource references have been added to the article, along with references from the Machines journal related to ADAMS kinematic simulation and relevant to this paper. （27-28）
The revised full text has been submitted, and the modified parts have been highlighted in red.
Thank you again for your review.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsThe revised version of the paper is suitable for publication in the journal.
Author Response
comments:The revised version of the paper is suitable for publication in the journal.
Response:Thank you for the reviewer's comments on this paper.I will submit the final version of the paper as soon as possible
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsThe revised version of the article has significantly improved and we feel that it can be published in the present form.
Comments on the Quality of English LanguageAlthough the language has improved, the sentence structure still needs some improvement. We feel that this will significantly improve the clarity of the paper.
Author Response
The English sentence structure in the paper has been revised, Thanks for your review comments.
Author Response File: Author Response.pdf
