Research on Machining Error Analysis and Traceability Method of Globoidal Indexing Cam Profile

Round 1

Reviewer 1 Report

As the Machines journal the topic of the work at hand would appear to be an appropriate one. The article is related to the analysis of the accuracy of CNC machining of a five-axis cam with spatial undevelopable surface. The article also presents the practical aspect of research implementation.

In general, when assessing the work, it is written in a very good scientific style, the technical vocabulary used is appropriate, the developed drawings are very carefully presented directly referring to the description in the text.

The work does not have any significant imperfections, nevertheless, I would like to convey to the authors a few comments that they should pay attention to, even not necessarily in the area of the work being assessed.

The abstract is a little bit confuse and missis some information like more results and conclusions, I suggest to authors follow these rules:

- One or two sentences on BACKGROUND

- Two or three sentences on METHODS

- Less than two sentences on RESULTS

- One sentence on CONCLUSION

The keywords should be in alphabetical order

In section Introduction, the work should be supplemented with a few paragraphs related to five-axis machining, generally, the remainder the analysis of the literature is extensive, it refers to scientific sources.

Figure 2 is not legible, I recommend that you focus on editing section (b) and put there the appropriate markings of axis movements (linear and rotational).

Table 3, the figures are not very legible due to their size, maybe it's better to omit the table? Marking the vertical axis is puzzling. The coefficient of variation allows to assess the strength of differentiation of a given statistical community, demonstrating the strength of the variable, and also assesses the arithmetic mean. A high value of the coefficient indicates a strong differentiation, and vice versa. Should it be expressed in natural or ratio units, unless it is not a factor?

Chapter 4 is very interesting from the point of view of the practical implementation of research. Of course, an indication of runtime errors is provided for the precision cam mechanism. I believe that in connection with the research carried out, there should be a wider discussion related to the obtained results. The accuracy of the cam is important, but you should also pay attention to the component that works with the cam. Follower finger, its shape and the nature of cooperation can more influence the transmission error? It would be advisable to give a few paragraphs to this analysis - the discussion section is best suited for this.

Of course, the ultimately error analysis of globoidal cam can be used to change the machining strategy and increase the accuracy of the component. How, however, to maintain the indicated relationship and improve the machining? By improving one accuracy parameter, you can worsen the others much more - these are critical conclusions that are worth considering.

Author Response

Dear editor,

Thank you very much for giving us the opportunity to revise our manuscript entitled “Research on machining error analysis and traceability method of globoidal indexing cam profile”. We would like to express our gratitude to the editor and the anonymous reviewers for the time and effort spent in processing and improving our manuscript. Those comments are very valuable and helpful for revising and improving our manuscript, as well as the important guiding significance to our researches. We have studied those comments carefully and made extensive modifications on the original manuscript. All the revisions have been using the “Track Changes” function.

The main corrections and changes, as an item-by-item response to the reviewers’ comments, are as following:

Point 1: The abstract is a little bit confuse and missis some information like more results and conclusions, I suggest to authors follow these rules:

- One or two sentences on BACKGROUND

- Two or three sentences on METHODS

- Less than two sentences on RESULTS

- One sentence on CONCLUSION

The keywords should be in alphabetical order

 Response 1: The content of the abstract is planned, and the background, methods, results and conclusions are introduced respectively to ensure the normative content of the abstract. At the same time, we also reordered the keywords to ensure that the keywords are in alphabetical order. The specific modifications are as follows:

Abstract: The profile of globoidal indexing cam is a spatial undevelopable surface. It needs a special computer numerical control (CNC) machine tool to finish batch production, and its machining quality will be affected by the motion error of each part of the machine tool and the clamped positioning error of the workpiece. Firstly, the mathematical model of the error of the machine tool for machining the globoidal cam surface is derived, and the influence of the error of the machine tool for machining the globoidal cam surface is given; Secondly, an error tracking method for globoidal cam profile machining error based on error sensitivity coefficient grouping is proposed, which improves the data processing speed and the accuracy of the tracking results; Finally, the error analysis and traceability method of the globoidal cam is verified by experiments, and the error traceability results are fed back to the processing link. The machining quality of globoidal cam is improved by the error compensation, which provides the key technology for the integration of the design, manufacture and measurement of globoidal cam.

Keywords: error sensitivity; error traceability; globoidal indexing cam; machining error model;  multi-body theory.

Point 2: In section Introduction, the work should be supplemented with a few paragraphs related to five-axis machining, generally, the remainder the analysis of the literature is extensive, it refers to scientific sources.

Response 2: The relevant content about five-axis machining has been added, and a reference has been added. The specific additions are as follows:

Five-axis CNC machine tools are generally used for the machining of globoidal cam, so the processing strategy of five-axis CNC machine tools is extremely important. By optimizing the machining strategy, the machining quality of the workpiece can be improved. Amaia Calleja studied the optimal machining strategy for blade turning and milling, and tested different strategies and inclination angles to obtain the best blade machining parameters and toolpath strategies[5]. Therefore, in the manufacturing process, the CNC machine tool should be analyzed in detail to ensure the machining accuracy of the globoidal cam. It is of great practical significance to study the machining error and detection of globoidal cam [6-7].

Point 3: Figure 2 is not legible, I recommend that you focus on editing section (b) and put there the appropriate markings of axis movements (linear and rotational).

Table 3, the figures are not very legible due to their size, maybe it's better to omit the table? Marking the vertical axis is puzzling. The coefficient of variation allows to assess the strength of differentiation of a given statistical community, demonstrating the strength of the variable, and also assesses the arithmetic mean. A high value of the coefficient indicates a strong differentiation, and vice versa. Should it be expressed in natural or ratio units, unless it is not a factor?

Response 3: We have added labels for motion axes and machine tool components in section (b) of  Figure 2, and modified the inappropriate units in Table 3. All inappropriate fonts in the charts have been modified to ensure the readability of the charts.

Point 4: Chapter 4 is very interesting from the point of view of the practical implementation of research. Of course, an indication of runtime errors is provided for the precision cam mechanism. I believe that in connection with the research carried out, there should be a wider discussion related to the obtained results. The accuracy of the cam is important, but you should also pay attention to the component that works with the cam. Follower finger, its shape and the nature of cooperation can more influence the transmission error? It would be advisable to give a few paragraphs to this analysis - the discussion section is best suited for this.

Response 4: The discussion on the cooperation between the globoidal cam and the follower is added. Since this article is not the main study of this aspect, it is only a brief description. The specific additions are as follows:

6.Discussion

The globoidal cam indexing mechanism is mainly composed of globoidal cams, turntables, boxes, camshafts, turntable shafts, bearings and other components. The output accuracy of the globoidal cam indexing mechanism is related to the manufacture of each component and the assembly of each component. The error sources of the globoidal cam indexing mechanism are mainly the machining geometric errors of its components, as well as the assembly errors of the globoidal cam and the turntable, the camshaft, the turntable shaft and the box. These errors have an impact on the output motion accuracy of the globoidal cam indexing mechanism.

The machining error of the globoidal cam indexing mechanism is a major factor that affects the indexing accuracy of the globoidal cam indexing mechanism, and it is also a difficult factor to analyze. In this paper, the assembly of the indexing mechanism box is not carried out, and only the machining error of the globoidal cam profile and the center distance error are analyzed. The correlation between the machining error of globoidal cam and the transmission precision of the globoidal cam indexing mechanism, and the influence of the center distance adjustment on the transmission precision are found out. It provides a theoretical basis for designing the precision distribution, processing technology adjustment and formulating the precision index system of the special processing machine tool for globoidal cam.

Special thanks to your comments. We hope we can learn more from you.

Author Response File: Author Response.docx

Reviewer 2 Report

The paper is commendable, I only have some issues with the organization of it.

In the introduction section some info regarding the geometry of the globoidal cam should be presented. Now, the introduction section relies only on text information, and it is hard to follow.

Some more information about the function of the so-called precision turntable within the measuring systems would also increase the overall quality of the paper.

Author Response

Dear editor,

Thank you very much for giving us the opportunity to revise our manuscript entitled “Research on machining error analysis and traceability method of globoidal indexing cam profile”. We would like to express our gratitude to the editor and the anonymous reviewers for the time and effort spent in processing and improving our manuscript. Those comments are very valuable and helpful for revising and improving our manuscript, as well as the important guiding significance to our researches. We have studied those comments carefully and made extensive modifications on the original manuscript. All the revisions have been using the “Track Changes” function.

The main corrections and changes, as an item-by-item response to the reviewers’ comments, are as following:

Point 1: In the introduction section some info regarding the geometry of the globoidal cam should be presented. Now, the introduction section relies only on text information, and it is hard to follow.

 Response 1: In the introduction part, the information of globoidal cam profile and the effect of globoidal cam accuracy on the ATC are added. The specific additions are as follows:

The globoidal cam profile is a non-developable surface in space, which is difficult to process. The profile error of the globoidal cam will directly reduce the output accuracy of the ATC, and seriously affect the grasping and positioning accuracy of the manipulator.

Point 2: Some more information about the function of the so-called precision turntable within the measuring systems would also increase the overall quality of the paper.

Response 2: In the experiment part, the specifications of the turntable are explained in detail and how it works. The specific additions are as follows:

The turntable is controlled by a stepping motor, and a single-chip microcomputer is used as the main control chip of the stepping motor control system, and the rotation angle of the turntable is displayed in real time through a circular grating angle measurement system. It can meet the measurement requirements of TC40 and TC50 series of globoidal cams.

Special thanks to your comments. We hope we can learn more from you.

Author Response File: Author Response.docx

Reviewer 3 Report

Article in Machines Journal subject.

In paper authors propose a general method of globoidal indexing cam profile machining error analysis and traceability. According to the working principle of the globoidal cam machine, the mathematical model of the globoidal cam profile error is established by using the multi-body system theory.

Article good writing  need only some editorial changes. Please consider my remarks

Comment

An example you wrote

2.3 Profile Modeling and Error Sensitivity Analysis of Globoidal Cam

1) Modeling of globoidal cam profile

When deriving the globoidal indexing cam profile equation, there are three rectangular coordinate systems are established.

And also

The planning of the globoidal cam measurement characteristic line is as follows:

(1) Measuring characteristic lines in the dwell segments: ① [358°, 2°], four characteristic lines are planned with 1° as a unit; ② [52°, 122.5°], 10 characteristic lines are planned with 5° as a unit; ③ [237.5°, 308°], 10 characteristic lines are planned with 5° as a unit.

(2) Measuring characteristic lines in the indexing segments: ① [2°, 52°], 10 characteristic lines are planned with 5° as a unit; ② [122.5°, 237.5°], 23 characteristic lines are planned with 5° as a unit; ③ [308°, 358°], 10 characteristic lines are planned with 5° as a unit.

Next example

(1) Error evaluation of the characteristic line of the dwell segments

The characteristic line of the dwell segments is a straight line. Since the maximum error value of the straight line is generally at the endpoint, the two-point method is used to solve the error. The specific process is:

① Fit the measurement points to a straight line as the evaluation benchmark;

② Solve the coordinates of the endpoints of the theoretical characteristic line;

③ Find the distance from the two ends of the theoretical characteristic line to the actual characteristic line, and judge whether it is within the tolerance range.

This is difficult to read (1)  ①  …. Symbols without meaning

I propose use of bullet list  or discuss with editor to use 3 level numbering ( understand thait is outside of MDPI papers template) and bulleting

This way  article you improve of article readability

3.2.1 Error evaluation of the characteristic line of the dwell segments

The characteristic line of the dwell segments is a straight line. Since the maximum error value of the straight line is generally at the endpoint, the two-point method is used to solve the error. The specific process is:

• Fit the measurement points to a straight line as the evaluation benchmark;
• Solve the coordinates of the endpoints of the theoretical characteristic line;
• Find the distance from the two ends of the theoretical characteristic line to the actual characteristic line, and judge whether it is within the tolerance range.

 

Also I propose use of bulletin in conclusions

5. Conclusions

Based on the multi-body system theory, this paper establishes the profile error model

of the globoidal cam, evaluates and traces the error. The proposed method is applied to

the machining of the globoidal cam in the factory, which improves the machining quality

and provides a key technology for the integration of the design, manufacture and

measurement of the globoidal cam. The main conclusions can be summarized as follows:

• Based on the multi-body system theory, the special machine tool for globoidal cam machining is analyzed, and the error transfer matrix of globoidal cam machining is deduced. The machining error model of the globoidal cam is established, and a method for comprehensively analyzing the machine tool through the curve of the error sensitivity coefficient of the globoidal cam is proposed. Through the method, the influence law of each error on the globoidal cam profile can be obtained.
• By analyzing the characteristics of the globoidal cam profile, a method of segmental  measurement and error evaluation of the globoidal cam profile characteristic  line and grouping traceability of machining errors is proposed. The dwell segments adopt the two-point method, and the index segments adopt the minimum area method. According to the analysis results of the error sensitivity of the globoidal cam profile, the sequential quadratic programming method is used to trace the processing errors, which  improves the data processing speed and the accuracy of the traceability results.
• By building a measurement system for globoidal cam transmission accuracy and profile error, the method proposed in this paper is used to evaluate and trace the error of  the measurement results, and the machining error compensation of the machine tool is carried out according to the results of error traceability. The experimental results show  that the error evaluation and traceability method proposed in this paper can improve the  machining accuracy of the globoidal cam.

Author Response

Dear editor,

Thank you very much for giving us the opportunity to revise our manuscript entitled “Research on machining error analysis and traceability method of globoidal indexing cam profile”. We would like to express our gratitude to the editor and the anonymous reviewers for the time and effort spent in processing and improving our manuscript. Those comments are very valuable and helpful for revising and improving our manuscript, as well as the important guiding significance to our researches. We have studied those comments carefully and made extensive modifications on the original manuscript. All the revisions have been using the “Track Changes” function.

The main corrections and changes, as an item-by-item response to the reviewers’ comments, are as following:

Point 1: Article good writing need only some editorial changes. Please consider my remarks

Comment

An example you wrote

2.3 Profile Modeling and Error Sensitivity Analysis of Globoidal Cam

1) Modeling of globoidal cam profile

When deriving the globoidal indexing cam profile equation, there are three rectangular coordinate systems are established.

And also

The planning of the globoidal cam measurement characteristic line is as follows:

(1) Measuring characteristic lines in the dwell segments: ① [358°, 2°], four characteristic lines are planned with 1° as a unit; ② [52°, 122.5°], 10 characteristic lines are planned with 5° as a unit; ③ [237.5°, 308°], 10 characteristic lines are planned with 5° as a unit.

(2) Measuring characteristic lines in the indexing segments: ① [2°, 52°], 10 characteristic lines are planned with 5° as a unit; ② [122.5°, 237.5°], 23 characteristic lines are planned with 5° as a unit; ③ [308°, 358°], 10 characteristic lines are planned with 5° as a unit.

Next example

(1) Error evaluation of the characteristic line of the dwell segments

The characteristic line of the dwell segments is a straight line. Since the maximum error value of the straight line is generally at the endpoint, the two-point method is used to solve the error. The specific process is:

① Fit the measurement points to a straight line as the evaluation benchmark;

② Solve the coordinates of the endpoints of the theoretical characteristic line;

③ Find the distance from the two ends of the theoretical characteristic line to the actual characteristic line, and judge whether it is within the tolerance range.

This is difficult to read (1) ①…. Symbols without meaning

I propose use of bullet list or discuss with editor to use 3 level numbering (understand thait is outside of MDPI papers template) and bulleting

This way article you improve of article readability

3.2.1 Error evaluation of the characteristic line of the dwell segments

The characteristic line of the dwell segments is a straight line. Since the maximum error value of the straight line is generally at the endpoint, the two-point method is used to solve the error. The specific process is:

• Fit the measurement points to a straight line as the evaluation benchmark;
• Solve the coordinates of the endpoints of the theoretical characteristic line;
• Find the distance from the two ends of the theoretical characteristic line to the actual characteristic line, and judge whether it is within the tolerance range.

 Response 1: In order to ensure the unity of full-text symbols, we modified some inappropriate symbols in the article according to the MDPI paper template. The revised result is as follows：

The characteristic line of the dwell segments is a straight line. Since the maximum error value of the straight line is generally at the endpoint, the two-point method is used to solve the error. The specific process is:

1. Fit the measurement points to a straight line as the evaluation benchmark;
2. Solve the coordinates of the endpoints of the theoretical characteristic line;
3. Find the distance from the two ends of the theoretical characteristic line to the actual characteristic line, and judge whether it is within the tolerance range.

The planning of the globoidal cam measurement characteristic line is as follows:

(1) Measuring characteristic lines in the dwell segments:

1. [358°, 2°], four characteristic lines are planned with 1° as a unit.
2. [52°, 122.5°], 10 characteristic lines are planned with 5° as a unit.
3. [237.5°, 308°], 10 characteristic lines are planned with 5° as a unit.

(2) Measuring characteristic lines in the indexing segments:

1. [2°, 52°], 10 characteristic lines are planned with 5° as a unit;
2. [122.5°, 237.5°], 23 characteristic lines are planned with 5° as a unit;
3. [308°, 358°], 10 characteristic lines are planned with 5° as a unit.

The characteristic line of the indexing segments is a curve, and the minimum area evaluation is used for error evaluation, as shown in Figure 6. The specific process is:

1. Use NURBS to fit the actual measurement points into a curve, as the error evaluation benchmark;
2. Solve the coordinates of the theoretical characteristic points;
3. Use the segmentation search method to determine the shortest distance from the theoretical characteristic point to the actual characteristic curve, and judge whether it is within the tolerance range.

Point 2: Also I propose use of bulletin in conclusions

5.Conclusions

Based on the multi-body system theory, this paper establishes the profile error model of the globoidal cam, evaluates and traces the error. The proposed method is applied to the machining of the globoidal cam in the factory, which improves the machining quality and provides a key technology for the integration of the design, manufacture and measurement of the globoidal cam. The main conclusions can be summarized as follows:

• Based on the multi-body system theory, the special machine tool for globoidal cam machining is analyzed, and the error transfer matrix of globoidal cam machining is deduced. The machining error model of the globoidal cam is established, and a method for comprehensively analyzing the machine tool through the curve of the error sensitivity coefficient of the globoidal cam is proposed. Through the method, the influence law of each error on the globoidal cam profile can be obtained.
• By analyzing the characteristics of the globoidal cam profile, a method of segmental  measurement and error evaluation of the globoidal cam profile characteristic  line and grouping traceability of machining errors is proposed. The dwell segments adopt the two-point method, and the index segments adopt the minimum area method. According to the analysis results of the error sensitivity of the globoidal cam profile, the sequential quadratic programming method is used to trace the processing errors, which  improves the data processing speed and the accuracy of the traceability results.
• By building a measurement system for globoidal cam transmission accuracy and profile error, the method proposed in this paper is used to evaluate and trace the error of the measurement results, and the machining error compensation of the machine tool is carried out according to the results of error traceability. The experimental results show that the error evaluation and traceability method proposed in this paper can improve the machining accuracy of the globoidal cam.

Response 2: First of all, thank you very much for your suggestions on the paper, but we have not revised the conclusion in consideration of the unity of the full text symbols, and still use the "(1)" notation form.

Special thanks to your comments. We hope we can learn more from you.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Paper can be published i present form