Modelling and Analysis of Dynamic Servo Error of Heavy Vertical Machining Centre Considering Nonlinear Factors
Round 1
Reviewer 1 Report
The manuscript presented a theoretical model for the servo feed system of a heavy-duty vertical machining centre. The influences of linear factors on dynamic servo error are considered. The stick-slip phenomenon is analyzed and verified via this theoretical model. The topic is meaningful to the parameter design and mechanical adjustments of the servo feed system. In all, minor revision is recommend.
The following issues should be addressed for further review or publication process.
1. Figure 9 missed the arrow of the feedback block P/2π.
2. The symbol of sign function is wrong in the equation 10.
3.Figure 11 is not clear enough to present the modeling of backlash. What does the block represent between the two bars?
4. The parameter symbols used in Table 3 are not consistent with those in the context. Please check them.
Minor editing of English language required.
Author Response
Manuscript ID: processes-2634562
Title: Modelling and Analysis of Dynamic Servo Error of Heavy Vertical Machining Centre Considering Nonlinear Factors
Response to Associate Editor
We would like to thank the editor for the high efficiency and great efforts on the manuscript. All the revisions made to the manuscript are marked up using the “Track Changes” function. The point-by-point response to the comments from the reviewers is listed as follows.
Response to Reviewers
We are very thankful for the valuable and constructive comments from the reviewers. We also appreciate the reviewers for their patient reviews. According to the comments, the paper has been carefully revised.
Reviewer #1:
Comment (1): Figure 9 missed the arrow of the feedback block P/2π.
Response (1): Thank you for pointing this out. Figure 9 has been updated in the revised version of the manuscript. Please check it.
Comment (2): The symbol of sign function is wrong in equation 10.
Response (2): Thanks for your feedback. The sign function in Equation 10 has been corrected.
Comment (3): Figure 11 is not clear enough to present the modeling of backlash. What does the block represent between the two bars?
Response (3): Thanks for your comment. Figure 11 has been modified. Please review it.
Comment (4): The parameter symbols used in Table 3 are not consistent with those in the context. Please check them.
Response (4): Thanks for your feedback. The parameter symbols you mentioned might be those in Table 1. The parameter symbols have been double checked and kept consistent with those in the context. Please review the changes in the revised manuscript.
Reviewer 2 Report
I've attached a PDF with my suggestions.
Comments for author File: 
Comments.pdf
Author Response
Manuscript ID: processes-2634562
Title: Modelling and Analysis of Dynamic Servo Error of Heavy Vertical Machining Centre Considering Nonlinear Factors
Response to Associate Editor
We would like to thank the editor for the high efficiency and great efforts on the manuscript. All the revisions made to the manuscript are marked up using the “Track Changes” function. The point-by-point response to the comments from the reviewers is listed as follows.
Response to Reviewers
We are very thankful for the valuable and constructive comments from the reviewers. We also appreciate the reviewers for their patient reviews. According to the comments, the paper has been carefully revised.
Reviewer #2:
Comment (1): The paper effectively communicates its findings. However some points show a weaker discussion because some works about stiffness of big lathes are not mentioned, and rigidity is key for long rams. In this way check the works Computation 2022, 10(12), 207; https://doi.org/10.3390/computation10120207 and the previous Analysis of the tool tip radial stiffness of turn-milling centers, The International Journal of Advanced Manufacturing Technology 60, 883-891.
Response (1): Thanks for your comment. The static stiffness and dynamic behavior of heavy-duty machine tools are also important factors that affect the tracking errors of the machine tools. The discussion has been included and the relevant citation has been used to support the discussion. Please review it.
Page 2, line 6: “When there is no tracking error in the servo axes, the multi-axis servo system will not exhibit a contour error. This is due to the fact that the tracking error is mainly affected by the closed-loop control and the hardware/machining conditions such as the static stiffness and the dynamic behavior of the servo system[6].”.
In Reference section: “[6] Lin, C.-Y.; Luh, Y.-P.; Lin, W.-Z.; Lin, B.-C.; Hung, J.-P. Modeling the static and dynamic behaviors of a large heavy-duty lathe machine under rated loads. Computation 2022, 10, 207.”.
Comment (2): If other CNC would be used, what things would change?
Response (2): Thanks for your question. In this paper, although the modelling of the driving system is based on the Siemens 840D CNC system, as illustrated in Figure 3, it’s worth noting that the fundamental structure of three-loop control is commonly used in other commercial CNC systems, such as FANUC, HEIDENHAIN and so on. Therefore, the simplification and modeling methods of CNC systems using the three-loop control structure are the same. However, the parameters and conversion coefficients in the practical CNC systems, which determine the parameter values in the simulation model, may vary depending on the specific CNC systems in use. The discussion has been included in the paper now.
Page 4, line 8: “This framework is commonly used in many commercial CNC systems, such as FANUC, HEIDENHAIN and so on. The parameters and conversion coefficients in the realistic CNC system, which determine the parameter values in the simulation model, might differ according to different CNC systems. Thus, the theoretical servo control model can be built based on this structure has certain universality.”
Page 26, line1: “The servo drive system model adopts a three-loop control structure commonly used in the commercial CNC systems, such as Siemens, FANUC, HEIDENHAIN.”
