Statistical Study of the Method of Radius-Change Sphericity Measurements
Round 1
Reviewer 1 Report
Interesting article, well organised. Some small mistakes could be improved:page 4 row136 form deviation not from deviation, row135 units have to use ISO Standards (2 inches)
Recommendation: instead of programme description in pages 4 and 5 for better understanding of difference between new and traditional methods an illustration could be more appropriate
Author Response
Firstly, I would like to thank you for the review of my manuscript.
Below you can find my response to your comments:
- Comment: “Interesting article, well organised. Some small mistakes could be improved: page 4 row136 form deviation not from deviation, row135 units have to use ISO Standards (2 inches)”
Answer: Thank you for your opinion. In the revision I have corrected the mistakes in rows 135 and 136
- Comment: “Recommendation: instead of programme description in pages 4 and 5 for better understanding of difference between new and traditional methods an illustration could be more appropriate”
Answer: I have decided to place the computer codes in the Appendix. In section 3 I have added a figure showing the difference between the traditional and the new strategy.
I hope that my response will be satisfying for you and my manuscript can be published owing to your valuable comments.
Best regards,
Krzysztof Stepien
Author Response File: 
Author Response.docx
Reviewer 2 Report
The equations for roundness and sphericity should be given and the differences described. Additionally, data using the traditional method should be taken using many different initial poses of the sphere so that a statistical variance can be determined with max and min values used to justify the variation in measurements on the new method. The same should be done for the new measurements so that the repeatability and variation can be assessed. If the initial pose does not cause a significant variation in the results then comparing old and new methods may be appropriate.
You claim to have 'more accurate results' but traceable standard spheres are not used to verify this. Simulations should be carried out for spheres having varied sphericity and form error components and varied initial poses for measurement.
There seems to be an underlying assumption that statistics can infer accuracy. Having measured all the samples and then using a program to decide the distribution type is irrelevant because the measurement of each sphere is done using both methods and can be compared directly.
In your conclusion you state that due to more area being assessed and high accuracy radius change measuring instrument then it is reasonable to assume that the the new method is more accurate. Assumptions of accuracy are not in line with traceability.
Discussion and references should be made to the "random ball test" for assessing sphericity.
Profile matching needs to be described.
Print is too small in Figure 1.
Research grants should be mentioned in acknowledgements not the main body.
Computer code should be in an appendix.
Author Response
Response to Reviewer’s comments:
Firstly, I would like to thank you for the review of my manuscript.
Below you can find my response to your comments:
- Comment: “The equations for roundness and sphericity should be given and the differences described.”
Answer: “The equations for roundness and sphericity have been added in Section 3.
- Comment: “Additionally, data using the traditional method should be taken using many different initial poses of the sphere so that a statistical variance can be determined with max and min values used to justify the variation in measurements on the new method. The same should be done for the new measurements so that the repeatability and variation can be assessed. If the initial pose does not cause a significant variation in the results then comparing old and new methods may be appropriate.”
Answer: We conducted our research in close cooperation with the Rolling Bearings Factory in Kraśnik. The aim of our research was to develop a method that will be applicable in production and will enable a more reliable assessment of form deviations of bearing balls. Therefore, in our research, we tried to compare our method and the traditional method in conditions as close to the industrial conditions as possible. In industrial conditions, roundness deviation is measured in a randomly selected cross-section and the initial pose is not the subject of interest. For this reason, we have not investigate the influence of the initial position of the ball on the measurement result. We were only interested to what extent the results obtained with our method would differ from the results obtained with the traditional method.
- Comment: “You claim to have 'more accurate results' but traceable standard spheres are not used to verify this. Simulations should be carried out for spheres having varied sphericity and form error components and varied initial poses for measurement.”
Answer: You are absolutely right – words “accurate” or “accuracy” are not suitable without any verification using traceable standard spheres. Therefore, I have removed them from the text of the manuscript. Generally I use terms “reliable”or “reliability” instead.
- Comment: “There seems to be an underlying assumption that statistics can infer accuracy. Having measured all the samples and then using a program to decide the distribution type is irrelevant because the measurement of each sphere is done using both methods and can be compared directly.”
Answer: Our aim was to study to what extent the results obtained with our method would differ from the results obtained with the traditional method. Statistical parameters can be useful to assess measurement accuracy or uncertainty (type A), however it was not the subject of this work. We are going to deal with the uncertainty evaluation in the near future.
- Comment: “In your conclusion you state that due to more area being assessed and high accuracy radius change measuring instrument then it is reasonable to assume that the the new method is more accurate. Assumptions of accuracy are not in line with traceability.””
Answer: Again, you are absolutely right about accuracy. It is not suitable term here, and I have replaced expression “more accurate” with “more reliable”
- Comment: “Discussion and references should be made to the "random ball test" for assessing sphericity.”
Answer: I have added the discussion and references referring to the “random ball test” in Section 2.
- Comment: “Profile matching needs to be described”
Answer: Profile matching has been described in Section 3.
- Comment: “Print is too small in Figure 1.”
Answer: Figure1 has been modified.
- Comment: “Research grants should be mentioned in acknowledgements not the main body..”
Answer: Information about the research grant has been removed from the main body
- . Comment: “Computer code should be in an appendix.”
Answer: Source codes of computer procedures have been given in an Appendix.
I hope that my response will be satisfying for you and my manuscript can be published owing to your valuable comments.
Best regards,
The Author
Reviewer 3 Report
This is quite interesting paper treating about the new concept of radius-change sphericity measurements. Below you will find a list of my negative remarks to the paper:
- Please change the number of the ‘Introduction’ section from 0 to 1.
- ‘Introduction’ section is very general and it does not present the investigated problem sufficiently. Please state clearly what is the research problem, how you intend to solve it and what is the novelty of your method.
- There are two sections numbered as ‘2’.
- Page 7, line 283, you write: “Results given in Tables 1 and 3 are presented graphically in Fig. 2 and Fig. 3.” should be: “Results given in Tables 1 and 2 are presented graphically in Fig. 2 and Fig. 3.”
- Page 9, line 320 it is not exactly sure what do you mean by: “Then the statistical parameters related to the values of the relative differences 321 between the results for both sets of parts.”
- What are the differences between 1st and 2nd sets of parts? What in your opinion may be the reason for different character of probability distributions of first and second set?
- Please add some directions for further development of presented system in ‘Conclusions’ section.
Author Response
Response to Reviewer’s comments:
Firstly, I would like to thank you for the review of my manuscript. Below you can find my response to your comments:
- Comment: “Please change the number of the ‘Introduction’ section from 0 to 1.
Answer: The number of the section “Introduction” was changed.
- Comment: “Introduction’ section is very general and it does not present the investigated problem sufficiently. Please state clearly what is the research problem, how you intend to solve it and what is the novelty of your method.”
Answer: Section “Ïntroduction” has been modified, we have added some background and the aim of our research, we have explained the research problem and how we had solved it.
- Comment: “There are two sections numbered as ‘2’”
Answer: The numbers of sections have been corrected.
- Comment: “Page 7, line 283, you write: “Results given in Tables 1 and 3 are presented graphically in Fig. 2 and Fig. 3.” should be: “Results given in Tables 1 and 2 are presented graphically in Fig. 2 and Fig. 3.””
Answer: The sentence has been corrected.
- Comment: “Page 9, line 320 it is not exactly sure what do you mean by: “Then the statistical parameters related to the values of the relative differences 321 between the results for both sets of parts.”
Answer: The sentence has been corrected.
- Comment: What are the differences between 1stand 2nd sets of parts? What in your opinion may be the reason for different character of probability distributions of first and second set?
Answer: Different character of probability distributions of the first and second set of the parts can be caused by the fact that in our experiment we have used bearing balls belonging to the technical class of accuracy. Form deviations of such parts may sometimes be quite large (reaching a few micrometers). Therefore, it was possible that some parts having large value of form deviation could significantly affect results of the analysis.
- Comment: “Please add some directions for further development of presented system in ‘Conclusions’ section”
Answer: We have added the direction for further development of presented system in the “Conclusions” – at this moment we are going to deal with uncertainty evaluation.
I hope that my response will be satisfying for you and my manuscript can be published owing to your valuable comments.
Best regards,
Krzysztof Stepien
Round 2
Reviewer 2 Report
You have made significant improvements in the article. However in order to make this more beneficial to readers a different kind of statistical evaluation needs to be provided. You have sufficient sets of data for each sphere to take all profiles from the set for each sphere and obtain an average value, a maximum value and a minimum value for the roundness as well as a standard deviation of all roundness values. Having this data, Each graphical display of "old" method data should include a max, min and +/- 2 (or 1) standard deviations and the average value for each bearing (sphere). From this data the reader can see that the value that they get may be very dependent on how the sphere is oriented initially. Then these parameters may be compared to the sphericity showing that the sphericity is a more consistent way of evaluating the manufacturing process. The data analysis that you have shown is to dependent on the initial orientation and should not be considered rigorous enough to establish better/worse reliability.
Fix the "XX" in the text.
Author Response
The response in attachment.
Author Response File: 
Author Response.pdf
