Digital Twin-Driven Thermal Error Prediction for CNC Machine Tool Spindle
Round 1
Reviewer 1 Report
The article proposes a numerical approach for thermal error prediction based on digital twins. The stated problem is topical to ensure the reliability of cutting processes during parts machining. The results could improve the spindle’s thermal error prediction accuracy.
However, despite the potential significance of the proposed study, the following flaws should be eliminated before recommended for publication:
1. Since the numerical model (1)–(6) is well-known, the authors should indicate the novelty of the applied approach.
2. The mathematical model of thermal state evaluation (7)–(17) is also well-known. Therefore, what is the scientific novelty of the approach?
3. The authors consider the heat conductivity differential equation (20). In this regard, the question is, why criteria dependencies (17) were applied? Also, where are the boundary conditions and a partial solution for equation (20)?
4. What state (stationary or non-stationary) was considered during the mathematical modeling (20)? If stationary, what limitations of time-domain temperature distribution were considered? In non-stationary, why did FEA not consider it?
5. The integral solution (25) considers the single-axis thermal state. This case can be considered for the uniform thermal distribution through the radius of the workpiece. So, please describe the limitations of this model (e.g., diameter to length ratio and others).
6. Since the previous comments, there is still an inconsistency between analytical modeling (algebraic, criteria, and differential equations), numerical simulations (ANSYS), and LSTM modeling. All these parts should be in precise accordance while describing the thermal mode, its boundaries and limitations, and a comparative analysis of the results.
7. The r-Pearson correlation coefficient (26) is a commonly applied similarity factor for measuring a linear correlation. The authors should present the correlation curve “E – x” with experimental dots and the evaluated approximation. Also, the question is, what limitations were considered to avoid the nonlinearities in the proposed model?
8. The analysis of the experimental results should be extended significantly. First, the authors should indicate the quantitative evaluation of the predicted parameters compared with the actual. Second, please compare the results with the results of other scientists worldwide, e.g., [14], [18], and [22]. Moreover, summarizing different approaches and their accuracy in a table will improve the representation of the results.
9. The conclusions are declarative since no limitations for the applied approach were indicated, and no ways for practical implementation were indicated. Moreover, ways for further studies should be announced.
There are no additional comments about the quality of the English language.
Author Response
Dear Reviewer and Editor,
Thanks for your reviews and comments. We carefully studied them and made additions and corrections in the revised version. Below is the response letter, the modifications are in the new version.
Author Response File: 
Author Response.docx
Reviewer 2 Report
The paper proposes a new method for predicting thermal errors in CNC machines. The method combines the simulation capabilities of a digital twin with the data processing abilities of a long-short-term-memory (LSTM). The digital twin system is used to obtain the theoretical values of thermal error, while the LSTM model is used to generate actual values based on experimental data. The particle swarm optimisation algorithm is then used to fuse the theoretical and actual values.
The work should be of interest to readers of the journal and could be accepted subject to minor corrections as detailed below.
1. The apostrophe (') in the title of the paper should be removed.
2. The authors should justify their adoption of the PSO algorithm instead of other optimisation algorithms.
3. The authors should add details to Figure 2 to make it self-explanatory. For example, they should specify 'Actual value' and 'Theoretical value' (value of which variable?). Similarly, more details could be added to Figure 3 (for example, by giving labels to the different arrows).
4. The authors should give standard textbook references for many of the equations in the paper.
5. Line 306: The authors should check the number of temperature measurement points. Is it nine or seven (T0 to T6)?
6. The authors should discuss the limitations of their technique and suggest future research directions.
The paper would benefit from further proofreading by a technically qualified native English speaker or a professional technical editor.
Author Response
Dear Reviewer and Editor,
Thanks for your reviews and comments. We carefully studied them and made additions and corrections in the revised version. Below is the response letter, the modifications are in the new version.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
The authors revised the manuscript essentially. Most of the comments and recommendations were considered. The article can be considered for publication.
