An Improved Cutting Force Model for Ultrasonically Assisted Grinding of Hard and Brittle Materials

Round 1

Reviewer 1 Report

The work is devoted to the issues of modeling ultrasonically assisted grinding of hard and brittle materials. The model takes into account the shape of the tool and the interaction of individual abrasive grains and their involvement in the material removal process, taking into account the oscillations.

The article is full of mathematical equations, symbols and indices. The big drawback is the lack of a list of symbols and abbreviations. In the list of symbols and in models, there should be consistency of conversion units (e.g. millimeters and micrometers).

Captions under figures require a more careful description.

Chapters 3 and 4 present 2 experiments that almost overlap. The experiments are used to verify the model. The research methodology should be supplemented with the accuracy of the measurement systems (force and amplitude of vibrations) and the measured data (raw data, repetitions, dynamics).

The K and Ks coefficients were determined from the force measurements for the first experiment. The K factor was modeled (equation 31) as dependent on A and rc. Three coefficients were identified for the equation. In the opinion of the reviewer, the accuracy and sensitivity of the experimentally determined coefficients should be verified.

The second experiment was used to verify the force components model. The model and experimental data in the charts are convergent. This was to be expected due to the tuning of the equation of force with the coefficients K and Ks. At the same time, the authors present studies of other researchers that are more distant in the charts. This suggests that their results are closer to the experiment. To prove this, the research would have to be carried out under the same conditions.

The conclusions refer to the results of experimental research. The aim of the study should be referred more strongly: an improved cutting force model for ultrasonically assisted grinding of hard and brittle materials.

Author Response

Reviewer 1:

• The article is full of mathematical equations, symbols and indices. The big drawback is the lack of a list of symbols and abbreviations. In the list of symbols and in models, there should be consistency of conversion units (e.g. millimeters and micrometers).

 

The symbols that appear in the formula have been defined in a table.

[Page 13, Table 1]

 

Table 1. The units of parameters in the formulas.

Symbols	Definitions	Unit
A	Vibration amplitude	m
Ri	Inner radius of the tool	m
Ro	Outer radius of the tool	m
rc	Radius of the transition fillet	m
νF	Feed rate	m/s
ap	Cutting depth	m
f	Ultrasonic vibration frequency	Hz
nr	Rotation speed of the tool	r/min
KIC	Fracture toughness	Pa·m1/2
E	Elastic modulus	Pa
HV	Hardness	Pa
he	Protrusive height of the abrasive grains	m

 

 

• Captions under figures require a more careful description.

 

We checked every item of the checklist, and all the requirements were met.

See below for details

 

Captions under figures have been revised.

 

“Figure 15. Influences of input variables on the value of K and Ks.”

“Figure 17. Comparison of axial direction force between experimental results and predicted results. ”

“Figure 18. Comparison of feed direction force between experimental results and predicted results.”

 

• Chapters 3 and 4 present 2 experiments that almost overlap. The experiments are used to verify the model. The research methodology should be supplemented with the accuracy of the measurement systems (force and amplitude of vibrations) and the measured data (raw data, repetitions, dynamics).

 

Thanks for the reviewer's comments. The experimental setup has been modified.

 

[3.1 Experimental setup]

“A YDCB-05 piezoelectric dynamometer (DUT, China) was used to measure the cutting forces, the resolution is ±0.001N，both the linear error and the reproducibility error are less than ±1%. A LK- H025 laser displacement sensor (KEYENCE, Japan) was utilized to measure the vibration amplitude while the tool was in rotation, the repeat accuracy is 0.1μm.”

 

• The K and Ks coefficients were determined from the force measurements for the first experiment. The K factor was modeled (equation 31) as dependent on A and rc. Three coefficients were identified for the equation. In the opinion of the reviewer, the accuracy and sensitivity of the experimentally determined coefficients should be verified.

 

Thanks for the reviewer's comments, which have given me great inspiration.

In the process of obtaining K and Ks, these two literatures are referred to and cited in this paper. The experimental results of this paper are similar to those of the two papers. Therefore, these two coefficients are determined to be accurate. But a more rigorous and scientific approach to research is something we need to improve. In the future research, more attention will be paid to accuracy.

 

• The second experiment was used to verify the force components model. The model and experimental data in the charts are convergent. This was to be expected due to the tuning of the equation of force with the coefficients K and Ks. At the same time, the authors present studies of other researchers that are more distant in the charts. This suggests that their results are closer to the experiment. To prove this, the research would have to be carried out under the same conditions.

 

Thank you for your valuable suggestions. In this paper, the influence of transition fillet radius on ultrasonic assisted grinding force was studied by cutting force model. Therefore, the parameters selected are not exactly the same as those in other tests. In particular, the grinding depth parameter must be larger than the fillet radius of the grinding wheel, so the parameter value of the grinding depth selected is much larger. But the range of other parameters is basically the same.

 

[Page 18, Paragraph 1 in the revised manuscript]

“Based on the results of the experiment with the input variables in Table 4, the values of the correction parameters in the model of Zhang [22] and Xiao [25] can be recalculated. Then, the cutting forces can be predicted though their models. Since the model in this paper is based on the fillet radius of the grinding wheel, the selected grinding depth is larger than the fillet radius of the tool, so the grinding depth parameter is larger, but the range of other parameters is basically the same.”

 

• The conclusions refer to the results of experimental research. The aim of the study should be referred more strongly: an improved cutting force model for ultrasonically assisted grinding of hard and brittle materials.

 

 

Thank you for your advice. The conclusions have been revised

 

[Paragraph 1 in Conclusions]

 

“A predictive cutting force model has been developed with the consideration of the in-fluence of the diamond grains in the transition fillet surface of the tool for predicting cut-ting forces in UAG. During the calculation of the cutting force, volume correction parameters K and Ks are used for the consideration of the overlapping of the removed volume of material and various protrusive heights. Through the slot grinding experiments, the values of K and Ks are obtained, and the influences of input variables and the radius of the transition fillet on the cutting forces have been studied both theoretically and experimentally. Some conclusions can be summarized from this study,”

Author Response File: Author Response.doc

Reviewer 2 Report

The reviewer comments of the paper «An improved cutting force model for ultrasonically assisted grinding of hard and brittle materials»- Reviewer

The authors presented an article «An improved cutting force model for ultrasonically assisted grinding of hard and brittle materials». However, there are several points in the article that require further explanation.

Comment 1:

The abstract needs to be completed.

Demonstrate in the abstract novelty, practical significance. Add quantitative and qualitative work results to the abstract. What is the error of the proposed cutting force model?

Comment 2:

The introduction of the article should be significantly expanded and improved.

Give briefly the relevance of the studied alloys. What properties do they have? What products are made from them? What problems with machinability are present.

Authors should take a closer look at the cutting force model for ultrasonically assisted grinding and show "white" spots. Which has not been previously investigated by other scientists.

For now, this article only covers articles from the 1980s to 2014s.

Authors should review at least 10 articles by renowned authors on UAG published in the last 5 years.

Among such article, add the following:

Journal of Friction and Wear 2016, 37(1), 60-65. doi:10.3103/S106836661601013X

Following the purpose of the article, briefly describe what has been done in each section of the article.

Comment 3:

2. Model Development

Are all the formulas in the article original? If not needed appropriate citations.

Are all the figures in the article original? If not needed appropriate citations and publisher permissions.

Comment 4:

3. Obtaining K and Ks

For devices, software and machines used in research, indicate in parentheses (manufacturer, city, country).

Comment 5:

It will be useful to add a section of Nomenclature in which to sign all the physical quantities and abbreviations encountered in the article. There are many physical quantities in the text and such a section will help to find the description of the necessary element.

For example,

a_p              : Depth of cut (mm)

UAG         : Ultrasonically assisted grinding

etc.

Comment 6:

The conclusions need to be improved.

What is the novelty of the article? What is the practical significance? What are the differences from previous works? What is the error of the proposed cutting force model?

Provide quantitative and qualitative conclusions for each parameter under study.

Conclusions should reflect the purpose of the article.

Comment 7:

Need thorough proofreading of English by a native speaker.

 

The article is interesting. However, the article needs to be improved. Authors should carefully study the comments and make improvements to the article step by step. All changes should be highlighted in color. After major changes can an article be considered for publication in the "Applied Sciences".

Author Response

Reviewer 2:

 

• The abstract needs to be completed. Demonstrate in the abstract novelty, practical significance. Add quantitative and qualitative work results to the abstract. What is the error of the proposed cutting force model?

 

The Abstract section has been modified.

[Abstract]

“The study demonstrates that the fillet radius is an important factor affecting the grinding force. With an increase in fillet radius from 0.2 to 1.2mm, grinding force increases by 139.6% in the axial direction and decreases by 70% in the feed direction. The error of the proposed cutting force model is 10.3%, and the experimental results verify the correctness of the force model.”

 

• The introduction of the article should be significantly expanded and improved.

 

Give briefly the relevance of the studied alloys. What properties do they have? What products are made from them? What problems with machinability are present.

Authors should take a closer look at the cutting force model for ultrasonically assisted grinding and show "white" spots. Which has not been previously investigated by other scientists.

For now, this article only covers articles from the 1980s to 2014s.

Authors should review at least 10 articles by renowned authors on UAG published in the last 5 years.

Among such article, add the following:

Journal of Friction and Wear 2016, 37(1), 60-65. doi:10.3103/S106836661601013X.

Following the purpose of the article, briefly describe what has been done in each section of the article.

 

Thanks for the reviewers' valuable suggestions. The introduction has been modified.

[Page 2, Paragraph 2 in the revised manuscript]

“The K9 optical glass is a typical hard and brittle material that is difficult to process. Extensive research demonstrates that UAG can effectively reduce tool wear and suppress breakage in machining of hard and brittle materials at a high machining efficiency and reduced material damage [3,4].”

[Page 3, Paragraph 1 in the revised manuscript]

“In this paper, an improved mechanistic model for predicting cutting forces based on the K9 optical glass in UAG is developed by considering the influence of the diamond grains in the transition fillet surface for the first time.”

 

[6] Yan, Y.; Zhang, Y.; Zhao, B.; Liu, J. Surface Formation and Damage Mechanisms of Nano-ZrO2 Ceramics under Axial Ultrasonic-Assisted Grinding. J. Mech. Sci. Technol. 2021, 35, 1187–1197. [https://doi.org/10.1007/s12206-021-0232-x]

[7] Wu, B.; Zhao, B.; Ding, W.; Su, H. Investigation of the Wear Characteristics of Microcrystal Alumina Abrasive Wheels during the Ultrasonic Vibration-Assisted Grinding of PTMCs. Wear. 2021, 203844. [https://doi.org/10.1016/j.wear.2021.203844]

[18] Li, C ; Zhang, F; Meng, B et al. Material removal mechanism and grinding force modelling of ultrasonic vibration assisted grinding for SiC ceramics. J. Ceram Int. 2016, 43,2981-2993. [https://doi.org/10.1016/j.ceramint.2016.11.066]

[19] Pereverzev, P. P.; Pimenov, D. Y. A Grinding Force Model Allowing for Dulling of Abrasive Wheel Cutting Grains in Plunge Cylindrical Grinding. J. Frict. Wear .2016, 37, 60–65. [https://doi.org/10.3103/S106836661601013X]

[23] Wu, C.; Li, B.; Yang, J.; Liang, S. Y. Prediction of Grinding Force for Brittle Materials Considering Co-Existing of Ductility and Brittleness. Int. J. Adv. Manuf. Technol. 2016, 87, 1967–1975. [https://doi.org/10.1007/s00170-016-8594-4]

[24] Li, Z.; Zhang, F.; Luo, X.; Guo, X.; Cai, Y.; Chang, W.; Sun, J. A New Grinding Force Model for Micro Grinding RB-SiC Ceramic with Grinding Wheel Topography as an Input. Micromachines 2018, 9 (8). [https://doi.org/10.3390/mi9080368]

 

18. Li, C ; Zhang, F; Meng, B et al. Material removal mechanism and grinding force modelling of ultrasonic vibration assisted grinding for SiC ceramics. J. Ceram Int. 2016, 43(3):2981-2993. [https://doi.org/10.1016/j.ceramint.2016.11.066]

 

• Model Development

Are all the formulas in the article original? If not needed appropriate citations.

Are all the figures in the article original? If not needed appropriate citations and publisher permissions.

 

Some unoriginal formulas and figures have been appropriate cited in the article.

 

 

• Obtaining K and Ks

For devices, software and machines used in research, indicate in parentheses (manufacturer, city, country).

 

Thanks for the reviewers' valuable suggestions. The content has been modified.

 

[3.1 Experimental setup]

“A YDCB-05 piezoelectric dynamometer (DUT, China) was used to measure the cutting forces, the resolution is ±0.001N，both the linear error and the reproducibility error are less than ±1%. A LK- H025 laser displacement sensor (KEYENCE, Japan) was utilized to measure the vibration amplitude while the tool was in rotation, the repeat accuracy is 0.1μm.”

 

• It will be useful to add a section of Nomenclature in which to sign all the physical quantities and abbreviations encountered in the article. There are many physical quantities in the text and such a section will help to find the description of the necessary element.

For example,

ap              : Depth of cut (mm)

UAG         : Ultrasonically assisted grinding

etc.

 

The symbols that appear in the formula have been defined in a table.

[Page 13, Table 1]

 

Table 1. The units of parameters in the formulas.

Symbols	Definitions	Unit
A	Vibration amplitude	m
Ri	Inner radius of the tool	m
Ro	Outer radius of the tool	m
rc	Radius of the transition fillet	m
νF	Feed rate	m/s
ap	Cutting depth	m
f	Ultrasonic vibration frequency	Hz
nr	Rotation speed of the tool	r/min
KIC	Fracture toughness	Pa·m1/2
E	Elastic modulus	Pa
HV	Hardness	Pa
he	Protrusive height of the abrasive grains	m

 

 

• The conclusions need to be improved.

What is the novelty of the article? What is the practical significance? What are the differences from previous works? What is the error of the proposed cutting force model?

Provide quantitative and qualitative conclusions for each parameter under study.

Conclusions should reflect the purpose of the article.

 

The conclusions have been revised.

 

[5 Conclusions]

 

“A predictive cutting force model has been developed with the consideration of the in-fluence of the diamond grains in the transition fillet surface of the tool for predicting cut-ting forces in UAG. During the calculation of the cutting force, volume correction parame-ters K and Ks are used for the consideration of the overlapping of the removed volume of material and various protrusive heights. Through the slot grinding experiments, the val-ues of K and Ks are obtained, and the influences of input variables and the radius of the transition fillet on the cutting forces have been studied both theoretically and experimen-tally. Some conclusions can be summarized from this study,

(1) Due to the variations in the normal and the tangential directions of the ultrasonic vibration amplitude, the cutting force of an abrasive grain in the transition fillet surface is a sum of the cutting forces produced by the former two modes of actions. In this paper, the cutting force model is established with the simultaneous consideration of the influence on the cutting force produced by the diamond grains in the end face, lateral face and transi-tion fillet surface of the tool. Through the slot grinding experiments with different input parameters, the trend in the cutting force determined by the model agrees well with that by the experiments. The error of the proposed cutting force model is 10.3%, and the experi-mental results verify the correctness of the force model. The improved cutting force model can be used for research of ultrasonically assisted grinding of hard and brittle materials.

(2) All the input parameters ( nr , A , vF , ap , rc ) have minor effect on the value of Ks , which is basically a constant with a value of 0.166., but only nr , vF and ap have minor ef-fects on K , which is basically a constant with a value of 0.37. However, vibration ampli-tude A and radius rc have a strong effect on the values of K. The value of K increases as amplitude A increases, but decreases as radius rc increases. A equation is used to express the relationship between K and the input variables A and rc.

(3) As the fillet radius increases from 0.2 to 1.2 mm, cutting force increases by 139.6% in the axial direction and decreases by 70% in the feed direction. As the spindle speed and ultrasonic vibration amplitude increase, both the axial and feed forces decrease. Further-more, the effect of ultrasonic vibration amplitude on the axial force is gradually reduced as the vibration amplitude gets larger, but is increased on the feed force. The cutting force in-crease as feed rate and cutting depth increase.”

 

 

 

• Need thorough proofreading of English by a native speaker.

 

The language of the paper has been corrected.

Author Response File: Author Response.doc

Round 2

Reviewer 2 Report

The authors have improved the article according to the comments. However, it is important to exclude group citations. [2.5-8] [14-19] [20-24] [29-31]. These proposals should be broken down into several. As an option ... [...], ... [...], ... [...].
After elimination of this, the article can be accepted.

Author Response

Thank you for the comments

• The authors have improved the article according to the comments. However, it is important to exclude group citations. [2.5-8] [14-19] [20-24] [29-31]. These proposals should be broken down into several. As an option ... [...], ... [...], ... [...].

After elimination of this, the article can be accepted.

 

Thanks for the reviewer's suggestions. The group citations have been excluded.

 

[Page 2, Paragraph 3 in the revised manuscript]

“Ultrasonically assisted grinding (UAG) is traditionally a hybrid machining process in which ultrasonic vibration is imposed on a grinding tool or workpiece for alternative material removal mechanisms [1]. UAG has become one of the advanced processing tech-niques for the advanced machining processes in machining of hard and brittle materials. The advantages include: reduced grinding force[5], reduced grinding temperature[6], re-duced surface and subsurface damage[7,8], etc.”

 

[Page 2, Paragraph 5 in the revised manuscript]

“In the existing literature, there are extensive studies on modelling material removal rate during UAG [14]. Pei [15] proposed a modeling method of material removal rate based on ultrasonic machining of ceramic materials, and carried out experimental verifi-cation, and further deduced the relationship between material removal rate and machin-ing parameters. Lee [16] deduced the model of cutting force and material removal rate of ultrasonic machining ceramic matrix composites, and verified that the increase of ma-chining parameters would lead to the increase of material removal rate and the coarsen-ing of the machined surface. Pei [17] proposed an approach to modeling the ductile-mode removal in rotary ultrasonic machining. Li [18] carried on a varied-depth nano-scratch test of single grain on a nano indentation system, and based on the varied-depth nano scratch test and the grain trajectory of ultrasonic vibration assisted grinding (UVAG), a theoretical model of the normal grinding force is acquired using the material removal in unit time as a bridge. Pereverzev [19] developed the mathematical model of cylindrical grinding, and obtained the grinding wheel blunt and abrasive removal rate.”

[Page 2, Paragraph 6 in the revised manuscript]

“However, there are few reports on predictive models of cutting forces during UAG of hard and brittle materials. During the axial ultrasonically assisted grinding, the diamond grains in the end face of a tool is forced to generate the intermittent hammering action [12,15]. Based on the impulse theory and brittle fracture theory, Pei et al. established a cutting force model of core tool for machining holes and tested it on titanium alloy [20], hard and brittle materials [21] and composite materials [22] with the rotary UAG. Wu [23] proposed a grinding force model considering both ductile removal force and brittle removal force., which was verified by experiments. Li [24] developed a grinding force model for micro-grinding of reaction-bonded silicon carbide ceramics.”