Optimal Design Method for Static Precision of Heavy-Duty Vertical Machining Center Based on Gravity Deformation Error Modelling
Round 1
Reviewer 1 Report
The authors presented a precision design method for heavy-duty vertical machining centers based on gravity deformation error modelling. Component stiffness coefficients and volume coefficients are introduced in the error budget process, which is different from the existed precision design methods and interesting to deal with the gravity-deformation-error-involved precision design issues. The topic is meaningful to the design for heavy-duty machine tools. Therefore, I recommend to a minor revision for this manuscript.
Here are some suggestions for the authors:
1. The specific features of heavy-duty machine tools need more explanation to show the differences of the proposed precision design method.
2. Please make the positive and negative directions of each motion axis clear in Figure 2.
3. Please add the unit of the precision design results to the label of the vertical axis in Figure 7.
4. There is an extra dash line in Line 211.
5. Some grammatical mistakes are found, such as the sentence in Line 376.
Author Response
We are very thankful for the valuable and constructive comments. We also appreciate for your patient reviews. According to the comments, the paper has been carefully revised. Below is our point-by-point response..
Comment (1): The specific features of heavy-duty machine tools need more explanation to show the differences of the proposed precision design method.
Response (1): The precision design problem raised by the specific characteristic of heavy-duty machine tools are emphasized in the introduction. The following changes can be tracked in the revised manuscript.
Line 39~41: “The influence of gravity-induced deformation error on machining precision is more prominent and significant than common CNC machine tools, occupying a larger proportion of the static errors [2].”
Line 84~87: “But for heavy-duty machine tools, the effects of the gravity make this precision requirement not optimal anymore. According to the precision requirement optimized without the consideration of the gravity-induced deformation error, it will be costly if the insurance of the machine tool precision only occurs at the assembly stage.”
Comment (2): Please make the positive and negative directions of each motion axis clear in Figure 2.
Response (2): The positive and negative directions of each motion axis are marked up in the new Figure 2.
Comment (3): Please add the unit of the precision design results to the label of the vertical axis in Figure 7.
Response (3): Since linear error components and angular error components are involved in the precision design results in Figure 7, the unit “mm/mrad” is added to the label of the vertical axis. In addition, the unit is also clarified in Table 2, Table 4 and Table 5.
Comment (4): There is an extra dash line in Line 211.
Response (4): Thanks for your correction. The manuscript has been doublechecked just in case there are still some format mistakes in the revised manuscript.
Comment (5): Some grammatical mistakes are found, such as the sentence in Line 376.
Response (5): Thanks for your correction. The text is revised as:
Line 384: “The calculations are given in Equation (17).”
The manuscript has been doublechecked just in case there are still some typo or English language mistakes in the revised manuscript.
Reviewer 2 Report
The article entitled "Optimal Design Method for Static Precision of Heavy-duty Vertical Machining Centres Based on Gravity Deformation Error Modelling" presents an interesting and up-to-date topic on machining accuracy. The paper is based on theoretical calculations while references to workshop practice are missing.
Specific comments:
In the article it is used many symbols for ease in the paper may be included a list of symbols.
Figure 1 decision box lacks selection criteria what determines whether it is yes or no?
Tables 2, 3, 4, 5 should be included an additional column identifying units.
The conclusion is similar to the abstract, but it should be contained information about the effects obtained by applying the method described in the paper (what extent does the described method increase the accuracy of the machine tool) and a comparison of the magnitude of errors calculated with the method presented in the article with the values other errors occurring in machine tools.
Author Response
Please see the attachment.
Author Response File: 
Author Response.docx
Reviewer 3 Report
The topic is interesting and may be accepted after revision.
1. Expand literature review and write the research gap.
2. Improve results and discussion citing with previous literature.
3. Conclusion should be supported with data/results.
4. Add scope for future work.
5. Following literaute may be included pertaining to the research
(a) experimental investigation on hard turning using mixed ceramic insert under accelerated cooling environment
(b) Optimization of multiple performance characteristics in abrasive jet machining using grey relational analysis
(c) Response surface and artificial neural network prediction model and optimization for surface roughness in machining
(d) Investigation on surface quality characteristics with multi-response parametric optimization and correlations
Author Response
Thanks for your comments.
Comment (1): Expand literature review and write the research gap.
Response (1): We doublechecked the introduction part. The research gap is added to the revised manuscript as:
Line 84~88: “But for heavy-duty machine tools, the effects of the gravity make this precision requirement not optimal anymore. According to the precision requirement optimized without the consideration of the gravity-induced deformation error, it will be costly if the insurance of the machine tool precision only occurs at the assembly stage.”
The error allocation, which is a nonlinear optimization problem, is the key to the precision design. The performance prediction methods based on the surrogate models (e.g., response surface, artificial neural network) are also commonly used to effectively solve this kind of optimization problem pertaining to the research. Therefore, in the introduction, (c) is cited as a reference to expand our literature review.
Line 78~80: “The response surface and artificial neural network is also used to predict the performance of machine tool, helping to design the parameters of interest through optimization [21]”
Comment (2): Improve results and discussion citing with previous literature.
Response (2): In the comparative analysis, the budget results by the proposed method, i.e., GEM-PDM, and the existing method, i.e., PDM, are compared by the new Table 6 in view of the values of volumetric error. The comparative analysis is also quantitively complemented as:
Line 542~547: “Once the gravity deformation error is guaranteed by the error budget results, the geo-metric error caused by manufacturing is controlled as small as possible, or the big values of error may make the volumetric error exceed the precision requirement boundaries. That’s the reason why the volumetric error results calculated by the PDM are -0.0337mm, -0.0157mm and 0.040mm, close to the given boundaries. And the improvements of the volumetric error by the GEM-PDM are 84.0%, 87.3% and 0.1%.”
Comment (3): Conclusion should be supported with data/results.
Response (3): Data and results are added in the revised conclusion to show the effectiveness of the proposed method as:
Line 582~586: “The improvement of the volumetric error compared with those by the PDM are 84.0%, 87.3% and 0.1%. Once the gravity deformation error is guaranteed by the error budget results, the geometric error caused by manufacturing is controlled as small as possible by the GEM-PDM to limit the volumetric error, meeting the precision design requirement.”
Comment (4): Add scope for future work.
Response (4): We have added the following sentences:
Line 559~564: “It is noted that the stiffness coefficients and volume fraction of each components are selected as independent design variables. However, the structural stiffness should be correlated to the given volume fraction to some extent. To make the GEM-PDM more accurate and realistic for budgeting the error components of heavy-duty machine tools, the idea of topology optimization will be introduced to reveal the relationship between the element stiffness and volume fraction in the future work.”
Comment (5): Following literature may be included pertaining to the research
(a) experimental investigation on hard turning using mixed ceramic insert under accelerated cooling environment
(b) Optimization of multiple performance characteristics in abrasive jet machining using grey relational analysis
(c) Response surface and artificial neural network prediction model and optimization for surface roughness in machining
(d) Investigation on surface quality characteristics with multi-response parametric optimization and correlations
Response (5): This paper focuses on the static precision design method for heavy-duty machine tools considering the gravity deformation error modeling. The error allocation, which is a nonlinear optimization problem, is the key to the precision design. The performance prediction methods based on the surrogate models (e.g., response surface, artificial neural network) are also commonly used to effectively solve this kind of optimization problem pertaining to the research. Therefore, in the introduction, (c) is cited as a reference to expand our literature review.
Round 2
Reviewer 3 Report
The paper has been improved. However, some literatures pertaining to the performance prediction models are suggested to be incorporated so as exapand the literature review section of the manuscript.
1. Response surface methodology and genetic algorithm used to optimize the cutting condition for surface roughness parameters in CNC turning
2. Surface roughness model and parametric optimization in finish turning using coated carbide insert: Response surface methodology and Taguchi approach
3. A response surface methodology and desirability approach for predictive modeling and optimization of cutting temperature in machining hardened steel
4. Application of response surface methodology on investigating flank wear in machining hardened steel using PVD TiN coated mixed ceramic insert
5. Investigating machinability in hard turning of AISI 52100 bearing steel through performance measurement: QR, ANN and GRA study
6. A study on erosion performance analysis of glass-epoxy composites filled with marble waste using artificial neural network
Author Response
Dear Reviewer,
Thank you much for your suggestions.
The recommended papers are very interesting and mainly focus on the surface roughness /machining processes. However, we feel it is not appropriate that they are cited in this paper as this paper proposes a precision design method for heavy-duty vertical machining centers based on gravity deformation error modelling, which does not consider the surface roughness aspects. We will try to cite the recommended papers in our future relevant research publications.
Many thanks.
Yours faithfully,
Dr Tianjian Li
