The Unsteady-State Response of Tires to Slip Angle and Vertical Load Variations

Round 1

Reviewer 1 Report

See attached file.

Comments for author File: Comments.pdf

Author Response

Please see attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

The paper is very interesting. It concerns modeling interactions (lateral forces, moments) in the contact between the vehicle tire and road surface, taking into account unsteady states.

Looking at the profile of the "Machines" journal, I can say that the proposed article fits perfectly with that profile, especially "Vehicle Engineering" section.

The structure of the article is clear. A review of knowledge is presented, followed by theoretical considerations on the mathematical modeling of forces and moments, considering unsteady states in contact with the tire-road surface with analysis in the frequency domain. In these considerations, the Authors paid attention to the influence of dynamic deformations of the tire carcass. Then, experimental studies confirming the usefulness of the presented model (one of the presented) are presented at the level of compliance and applicability. The article is summarized with conclusions in which the main achievements were noted, and the directions of further research are indicated.

It can be concluded that the presented content provides a lot of interesting information on the problem of modeling contact forces and presents an experimentally verified model that can be enriched with standard tire models used in simulation studies of vehicle dynamics.

Below I indicate some reservations and comments that will help improve the quality and readability of the work or indicate minor editing flaws.

·       General – Knowledge overview: the literature review lacks reference to the fundamental positions in which the tire transient problem was first raised. I mean works::

-        von Schlippe B., Dietrich R., Zur Mechanik des Luftreifens Zentrale für Wissenschaftliches. Berichtswesen der Luftfahrtforschung. Berlin 1942.

-        Segel L., Force and moment response of pneumatic tires to lateral motion inputs. Transactions ASME. J. of Engineering for Industry, 88B, 1966

and later from the 80-90s of the 20th century:

-          Schieschke R., The importance of tire dynamics in vehicle simulation. Paper presented at The Tire Society. 9th Annual Meeting and Conference on Tire Science and Technology. Akron, Ohio, USA. March 20-21, 1990.

-          Schieschke R., Hiemenz R., The relevance of tire dynamics in vehicle simulation. XXIII FISITA Congress, Torino, Italy. May 711, 1990.

·       There are also no references to works presenting models that can be used in a complex model of vehicle dynamics (based on advanced experimental research): for example:

-      Luty W. Simulation research of the tire Basic Relaxation Model in conditions of the wheel cornering angle oscillations, IOP Conference Series: Materials Science and Engineering, 2016, nr 148, s.1-7. DOI:10.1088/1757-899X/148/1/012015 or

-      Luty W., Influence of the tire relaxation on the simulation results of the vehicle lateral dynamics in aspect of the vehicle driving safety. Journal of Kones Powertrain and Transport. No. 22, vol. 1/2015.

·       I also lack references to examples of works describing the importance of the description of transient states of tires in the simulation of car dynamics, for example:

Lozia Z., Is the representation of transient states of tyres a matter of practical importance in the simulations of vehicle motion. The Archives of Automotive Engineering, 2017; 77(3): 63-84, http://www.aaejournal.com/Is-the-representation-of-transient-states-of-tyres-a-matter-of-practical-importance,99445,0,2.html

Other:

·       Line 1: paper type is not selected.

·       Line 76: …theory. model is derived……. - "Model" in a capital letter

·       Fig. 1 and its description: It is a crucial Figure, but the description accompanying it is unclear. The description does not describe all the quantities appearing on it. Perhaps it is worth considering the presentation of this model in a few diagrams illustrating various elements of the model and with a broader description. A good understanding of this drawing is key to understanding further mathematical formalism.

·       The symbols w in Figure 1 and the following equations are "italic" but not in the main text. This should be unified.

·       line 117, 118: symbols Y_c, Y_t,  are not shown in Fig. 1 (see previous note)

·       Eq (4)-(9): symbols F_y, K_y, K_cb, ….and further are not explained. Their meaning can only be guessed from the rest of the text in the following chapters

·       line 137: there is no explanation why this form of equations (16), (17)

·       line 137, Eq. (16), (17): symbols V_r, V_x, are not explained.

·       Eq. (20): symbol C is not explained.

·       line 142: “when?” – lack of space.

·       Eq. (28), (29): “t’ ” - ?

·       line 185-187: „The following will show the unsteady frequency characteristic curves without considering the elasticity of the carcass and considering the complex deformation of the carcass:” The content should refer to specific numbers of figures or tables. For example: “The following figures (Fig. 2 and 3) show the unsteady frequency characteristic curves without considering the elasticity of the carcass and considering the complex deformation of the carcass.”. This remark also applies to the rest of the article.

·       Fig. 2-10: in figure captions, there is no information (legend) about the content of individual fragments of the figures – (a) ?   (b) ?

·       Fig. 2-10: what is “w_sa”?

·       Fig. 13: In fig. 13 appears the block labeled "UniTire Model / MF-Tire". People familiar with tire-road contact force modeling will probably guess what this means. However, others may find it incomprehensible. I propose to replace this description: "standard tire forces model, i.e. UniTire Model / Magic Formula Model" (or the like) and add information about it in the text describing this flowchart with an indication of references where UniTire M. and MF M. descriptions can be found.

·       line 404: “….Table 1 method….” – 1) rather should be: “quasi-steady-state cornering method (table 1) ….”; 2) Research method can make model more accurate? There is something wrong with that phrase.

·       Fig. 16: formatting error - figure divided into two pages

·       References: the way of writing the titles of the items should be unified: either "Very Important Article about Tires" or "Very important article about tires"

Author Response

Please see attachment.

Author Response File: Author Response.docx

Reviewer 3 Report

The paper introduce an extended model of the  unsteady-state response of tires to slip angle and vertical load variations. The work is interesting and the developed model is validated using experimental data. The results seems to be correct. There are, however, two issues to be attended: First in the introduction the claimed results are not discussed in the context of early results. Secondly, some minor issues to be cleared respect to the form of present the frequency response.

Author Response

Dear Reviewer,

Thank you very much for your attention and the valuable comments on our manuscript. The responses to the comments are listed below.

Comment 1: First in the introduction the claimed results are not discussed in the context of early results.

Response: Thank you very much for taking time to review the paper. The introduction was modified regarding your advice, and more detailed early researches have been added. 

Comment 2: Secondly, some minor issues to be cleared respect to the form of present the frequency response.

Response: Thank you very much for your advice. I have made some optimization on frequency response. Please view the revised manuscript.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The authors have improved the paper by citing significant work by other scholars. The presentation of the model has also been improved and the results are presented more clearly. Therefore, I recommend the paper for publication in its current form.