Design of a Longitudinal-Bending Elliptical Vibration Ultrasonic Transducer with a Bent Horn

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In the abstract you should not use A type and B type that are defined later in the paper.

line 67 correct "a design"

Give the reference for laser micrometer

Line 496 correct "fig15 shows"

In conclusion, you mention that the tool life is increased, how do you measure and define it?

Author Response

1. In the abstract you should not use A type and B type that are defined later in the paper.

Response: “A-type transducer can be used for UVAC of external surface, and B-type transducer can be used for UVAC of internal cavity. The maximum peak-peak amplitudes of longitudinal vibration and bending vibration for A-type transducer are 14μm and 16μm, respectively. The maximum peak-peak amplitudes of longitudinal vibration and bending vibration for B-type transducer are 17μm and 21μm, respectively. Such a large amplitude can fully meet the needs of UVAC. When using ultrasonic transducer with bending horn for partial separation continuous high-speed elliptic ultrasonic vibration cutting (HEUVC), compared with conventional cutting (CC), HEUVC can im-prove the tool life by 65.74% for A-type transducer, HEUVC can improve the tool life by 44.62% for B-type transducer.” has been revised to “The designed transducer can be used for partial separation continuous high-speed elliptic ultrasonic vibration cutting (HEUVC) of external surface and internal cavity. The ultrasonic vibration amplitude of the transducer can meet the needs of HEUVC. When using ultrasonic transducer with bending horn for HEUVC, compared with conventional cutting (CC), HEUVC can improve the tool life by about 50%.” (Lines 24-29)

2. line 67 correct "a design".

Response: It has been revised in the manuscript. (Line 83)

3. Give the reference for laser micrometer

Response: The explanation that " A Keyence LK-Navigator 2 laser micrometer is used to measure the amplitude and vibration direction of ultrasonic tool holder." has been added to the manuscript. (Lines 474-476)

4. Line 496 correct "fig15 shows".

Response: It has been revised in the manuscript. (Line 631)

5. In conclusion, you mention that the tool life is increased, how do you measure and define it?

Response: The explanation that " An Olympus BX51M microscope is used to measure tool wear. When the maximum flank wear VBmax = 0.3 mm, the cutting experiment is stopped, and the cutting distance at this time is the tool life under this cutting condition." has been added to the manuscript. (Lines 590-592)

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The article entitled “Design of longitudinal-bending elliptical vibration ultrasonic transducer with bending horn” is innovative enough. This article is acceptable after revision.

1. The article mentioned " When using ultrasonic transducer with bending horn for partial separation continuous high-speed elliptic ultrasonic vibration cutting (HEUVC), compared with conventional cutting (CC), HEUVC can improve the tool life by 65.74% for A-type transducer, HEUVC can improve the tool life by 44.62% for B-type transducer.". The article does not explain what partial separation continuous high-speed elliptic ultrasonic vibration cutting is, nor does it quote the relevant literature, please give an explanation.
2. Is the design error of the design method adopted in this paper reasonable? Please investigate similar research and explain! Discuss the influence of design error on transducer frequency matching.
3. The conclusion of the article is not summarized well, please summarize the conclusion part again.
4. There are too many paragraphs in the introduction. Can some parts be merged? Please summarize the introduction again.
5. Can you mark the direction of modal vibration with arrows in Figure 7, as the reader wants to see this information intuitively.
6. Some places in the article are written like Chinglish, please polish the article.

Author Response

1. The article mentioned " When using ultrasonic transducer with bending horn for partial separation continuous high-speed elliptic ultrasonic vibration cutting (HEUVC), compared with conventional cutting (CC), HEUVC can improve the tool life by 65.74% for A-type transducer, HEUVC can improve the tool life by 44.62% for B-type transducer.". The article does not explain what partial separation continuous high-speed elliptic ultrasonic vibration cutting is, nor does it quote the relevant literature, please give an explanation.

Response: The explanation that " In this paper, we propose partial separation continuous high-speed elliptical ultrasonic vibration cutting (HEUVC) method for cutting Inconel 718." has been added to the manuscript. (Lines 568-570)

The explanation that " Fig. 13 is a schematic diagram of dynamic process of wave-ridges extrusion and partial separation on rake face and flank face in orthogonal plane. Wave-ridges are periodic undulating structures generated in the direction of chip thickness or cutting thickness, including peaks and valleys. In a generation cycle of wave-ridges structure, there are two processes: wave-ridges extrusion and partial separation. In the process of wave-ridges extrusion, the tool extrudes the generated wave-ridges. In the process of partial separation, a separation gap is generated between the tool and the previously extruded wave-ridges. " has been added to the manuscript. (Lines 571-577)

2. Is the design error of the design method adopted in this paper reasonable? Please investigate similar research and explain! Discuss the influence of design error on transducer frequency matching.

Response: The explanation that " According to the literature research on the modal simulation of transducer, the error between the designed frequency and the measured frequency needs to be within 10%, and the design error in this paper meets the requirements. When there is a design error, it will not adversely affect the frequency matching of the transducer, because the measured frequencies of longitudinal vibration and bending vibration are all lower than the design frequency, and the decreased values are close." has been added to the manuscript. (Lines 468-473)

3. The conclusion of the article is not summarized well, please summarize the conclusion part again.

Response: The revised conclusion is as follows: " In this paper, a longitudinal-bending elliptical vibration ultrasonic transducer with bending horn and its design method are proposed. The application of the transducer solves the structural interference problem between the conventional ultrasonic tool holder and the workpiece in the process of UVAC. When matching the frequencies of longitudinal vibration and bending vibration in elliptical vibration ultrasonic transducer, firstly, the length of the horn is de-signed properly, so that there is a small difference between the frequencies of longitudinal vibration and bending vibration, and then the frequency of bending vibration is close to the frequency of longitudinal vibration by adjusting the section width of the horn. Finally, the longitudinal vibration and bending vibration are matched to one frequency by impedance matching. The proposed frequency matching theory can be well applied to the simulation design of transducers. The bending of the horn causes the asymmetry of the structure, which makes the vibration directions of bending vibration and longitudinal vibration incline to the bending direction of the horn. By adjusting the phase difference, the circular vibration trajectory of the tool tip can be obtained. HEUVC method can partially open the cutting area in the process of continuous cutting, so that the coolant can enter the cutting area to cool and lubricate the tool and workpiece, reduce the cutting temperature and cutting force, and thus prolong the tool life. Compared with CC, the main cutting force, axial thrust force and radial thrust force of HEUVC are reduced by 17.96%, 17.25% and 16.24% respectively when cutting with A-type transducer. Compared with CC, the main cutting force, axial thrust force and radial thrust force of HEUVC are reduced by 16.95%, 18.93% and 15.36% respectively when cutting with B-type transducer. Compared with CC, HEUVC can improve the tool life by 65.74% when cutting with A-type transducer. Compared with CC, HEUVC can improve the tool life by 44.62% when cutting with B-type transducer." (Lines 643-666)

4. There are too many paragraphs in the introduction. Can some parts be merged? Please summarize the introduction again.

Response: The revised introduction is as follows:" UVAC can reduce cutting temperature and cutting force and improve tool life and surface integrity by separation effect, so it is widely used in cutting difficult-to-machine materials [1-4]. However, the application of ultrasonic vibration-assisted turning in practical production is limited because the ultrasonic vibration turning tool holder will interfere with the parts in structure [5, 6]. The thin and straight horn of the ultrasonic transducer is located in the center of the thick transducer, so that the tool tip of the ultrasonic vibration turning tool holder cannot be located on the outermost side of the entire tool holder, which leads to the structural interference between the tool holder and the part during turning. In order to solve this problem, an ultrasonic vibration transducer with a bending horn must be designed for ultrasonic vibration-assisted turning. In traditional ultrasonic vibration cutting (UVC), the tool vibrates along the cutting speed direction, in elliptic ultrasonic vibration cutting (EUVC), the tool has vibration components along cutting speed and cutting depth. There is a critical cutting speed limit in UVC and EUVC, and the material removal rate (MRR) is low [7, 8]. Zhang et al. proposed high-speed ultrasonic vibration cutting (HUVC), which improved the cutting speed several times [9]. However, due to the limitation of critical feed, the MRR is also low. Zhang et al. [10] proposed partial separation continuous high-speed ultrasonic vibration cutting (C-HUVC), which solved the problem of low MRR in UVAC. UVAC methods include UVC, EUVC, and HUVC. When the tool vibrates along the cutting depth direction, the tool impacts the workpiece radially, which leads to a large impact force, so the tool wear is intensified. In HUVC and C-HUVC, the tool vibrates along the feed direction. When the tool vibrates along the cutting speed direction or the feeding direction, the tool impacts the metal of the cutting layer, and the impact force is small. However, when the tool vibrates along the cutting depth direction, the tool impacts the workpiece radially, which leads to a large impact force, so the tool wear is intensified. In UVC, the tool is prone to chip when it retreats. In EUVC, the impact on the tool is great. In HUVC and C-HUVC, the tool vibrations along the feed direction. However, when cutting complex parts, the vibration direction of the tool changes between the cutting depth and the feed direction. None of the above UVAC can be used for turning complex parts. It is necessary to develop an elliptic ultrasonic vibration cutting method in tool base surface with relatively small impact force on the tool. Therefore, it is necessary to design a longitudinal-bending elliptical vibration ultrasonic transducer with a bending horn for HEUVC. In the machining of parts, the step usually needs both cylindrical turning and face turning, and the tool with unidirectional vibration usually encounters the situation that the tool impacts the workpiece radially, so the mode of elliptical ultrasonic vibration in the base plane is adopted in this paper. The tool that vibrates elliptically in the base plane has vibration components along the feed and cutting depth. To solve the problems of conventional ultrasonic turning tool holder in terms of mechanical structure and machining technology, a longitudinal-bending elliptical vibration ultrasonic transducer with bending horn is proposed, which will be used for HEUVC." (Lines 34-73)

5. Can you mark the direction of modal vibration with arrows in Figure 7, as the reader wants to see this information intuitively.

Response: The explanation that " The direction of modal vibration is indicated by a red arrow in Fig. 7." has been added to the manuscript. (Lines 453-454)

6. Some places in the article are written like Chinglish, please polish the article.

Response: The language of the full text has been polished, and the following parts have been modified:

" Since 1975, HORTON et al. [11] proposed the use of piezosurgery for the treatment of oral diseases, today the piezosurgery with bending horn has been widely used in clinical practice [12-15]. " was revised to " Since 1975, HORTON et al. [11] introduced the concept of using piezosurgery for treating oral diseases. Today, piezosurgery with bending horns has become widely adopted in clinical practice [12-15]."(Lines 76-78)

" In this paper, firstly, through brief theoretical analysis, the relationship between the resonant angular frequency of longitudinal vibration and bending vibration in the beam and the structural size of the beam is determined, which provides a basis for ad-justing the structural parameters of the horn in the simulation design of ultrasonic transducer. Secondly, through induction and summary, the simulation design flow chart of longitudinal-bending elliptical vibration ultrasonic transducer with bending horn is put forward. Through the simulation design, the structural dimensions of the ultrasonic transducer are obtained. Finally, the correctness of simulation design is verified by vibration test, and the adaptability of ultrasonic transducer and the feasibility of cutting process are verified by cutting test." was revised to " In this paper, first, a brief theoretical analysis is conducted to determine the relationship between the resonant angular frequency of longitudinal and bending vibrations in a beam and its structural dimensions. This provides a basis for adjusting the horn's structural parameters during the simulation design of ultrasonic transducers. Second, through induction and summarization, a simulation design flowchart is proposed for longitudinal-bending elliptical vibration ultrasonic transducers with bending horns, enabling the acquisition of the transducer's structural dimensions via simulation. Finally, the accuracy of the simulation design is verified through vibration testing, while cutting tests confirm the adaptability of the ultrasonic transducer and the feasibility of the cutting process."(Lines 122-130)

" UVAC can periodically open the cutting area, which enables the coolant to enter the cutting area to lubricate the cooling tool and the machined surface, thus reducing the cutting temperature and cutting force and improving the tool life and surface in-tegrity, so it is widely used in cutting difficult-to-machine materials. There are many difficult-to-machine materials in aerospace field, and UVAC has broad application prospects. " was revised to " UVAC can periodically open the cutting area, allowing coolant to enter and lubricate both the tool and the machined surface. This reduces cutting temperature and force, ultimately improving tool life and surface integrity. As a result, it is widely used for cutting difficult-to-machine materials. Given the prevalence of such materials in the aerospace field, UVAC holds broad application prospects."(Lines 151-156)

" On the basis of obtaining the length of the horn, the influence of the width of horn d on the resonance frequency of longitudinal vibration and bending vibration is stud-ied. As can be seen from Fig. 4(b), with the increase of the width of horn, the resonant frequency of bending vibration increases obviously, while the resonant frequency of longitudinal vibration increases slightly. Therefore, the resonant frequencies of bending vibration and longitudinal vibration can be close by changing the width of horn." was revised to " Based on obtaining the length of the horn, the influence of the horn's width d on the resonance frequencies of longitudinal and bending vibrations is investigated. As shown in Fig. 4(b), as the horn's width increases, the resonant frequency of bending vibration rises significantly, whereas the resonant frequency of longitudinal vibration increases only slightly. Consequently, by adjusting the horn's width, the resonant fre-quencies of bending and longitudinal vibrations can be brought closer together."(Lines 345-351)

" It is difficult to open the cutting zone in continuous cutting, so high cutting temperature and cutting force limit the tool life when cutting difficult-to-machine materials. Intermittent UVAC can reduce the cutting temperature and cutting force by opening the cutting area to improve the tool life, so it is widely used in cutting difficult-to-machine materials." was revised to " It is challenging to open the cutting zone during continuous cutting, which results in high cutting temperatures and forces that significantly limit tool life when machining difficult-to-machine materials. Intermittent UVAC can decrease cutting temperature and force by opening the cutting area, thereby enhancing tool life and making it a popular choice for machining such materials. "(Lines 559-563)

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

In this paper, the authors present two types of longitudinal-bending elliptical vibration ultrasonic transducers with novel structural designs. Overall, the paper is well-organized and the topic is of interest. However, several descriptions are unclear or insufficiently detailed. A major revision is recommended before the paper can be considered for acceptance. Detailed comments are provided below:

1. The authors employ a simplified beam model for theoretical analysis. However, this model may not accurately reflect the actual structure of the transducers. For example, the parameter α in Type A and the parameter e in Type B likely influence both the resonant frequency and vibration mode. These effects are not discussed.
2. In Section 3.2 simulation design, the description of the piezoelectric ceramics used in the simulation is unclear. Line 186 mentions "four half-piece piezoelectric ceramic disks" and "two complete disks," but Figure 2 only shows four disks in total. Please clarify how many ceramics are used, what "half-piece" ceramics mean, and specify their polarization directions.
3. The meanings of the symbols θ and γ are not defined in the text. Please define these parameters and explain their physical significance and why these specific ranges were chosen.
4. All figures should include clear and complete captions for each subfigure (e.g., Fig. 2(a), Fig. 2(b), etc.) to enhance readability and understanding.
5. The criteria used for optimization are not well explained. For instance, why was the frequency range for Type A chosen as 16–22 kHz? Frequencies below 20 kHz are typically not considered ultrasonic. Additionally, the rationale behind selecting a θ–γ range of 60° to 120° should be discussed.
6. Please specify the software and modules used for simulation (e.g., ANSYS).
7. Stiffness is important for the cutting. Although the paper mentions stiffness, no simulation or quantitative analysis is presented. The authors should include stiffness analysis and discuss what stiffness values are required to meet machining needs.
8. For the modal analysis, did the authors fix the flange to simulate the actual vibration scenario?
9. Since two types of piezoelectric ceramics are used to excite the horn, this configuration should be reflected in the simulation setup. A simple modal analysis may not adequately represent the real vibration behavior under excitation.
10. The desired vibration mode appears at a relatively high modal order, which suggests it may not be the dominant mode. Please discuss the vibration efficiency and whether the mode can be effectively excited during operation.
11. The authors should describe the applied voltage, signal type, and configuration used for the two types of piezoelectric ceramics during vibration testing.
12. In Figure 9, the measured amplitudes are significantly higher than those in Figures 11 and 12. This discrepancy is confusing and should be addressed and explained.
13. Due to the discrepancy between the resonant frequencies of longitudinal and bending vibration, is there any potential for overheating on the horn?
14. In Figure 15, the machining results suggest that ultrasonic vibration may degrade surface quality, even though tool life is improved. Surface roughness should be quantitatively measured and reported.
15. Tool life alone is insufficient to demonstrate the benefits of the proposed design. It is recommended that cutting forces be measured and compared across conditions
16. Can the author explain why type A has a longer tool life than type B?

Comments on the Quality of English Language

Need to improve

Author Response

1. The authors employ a simplified beam model for theoretical analysis. However, this model may not accurately reflect the actual structure of the transducers. For example, the parameter α in Type A and the parameter e in Type B likely influence both the resonant frequency and vibration mode. These effects are not discussed.

Response: At present, it is difficult to establish the influence of the parameter α and e on the resonant frequency and vibration mode theoretically. We discussed the influence of parameter α on the resonant frequency and vibration mode through simulation. (Lines 389-409)

The explanation that " Reducing the value of parameter e will reduce the stiffness of the transducer, while increasing the value of parameter e will cause structural interference between the horn and the workpiece. The value of e of the ultrasonic transducer is kept the same as that of the conventional tool holder, so the influence of the parameter e on the resonant frequency and vibration mode is not discussed in this paper." has been added to the manuscript. (Lines 434-439)

2. In Section 3.2 simulation design, the description of the piezoelectric ceramics used in the simulation is unclear. Line 186 mentions "four half-piece piezoelectric ceramic disks" and "two complete disks," but Figure 2 only shows four disks in total. Please clarify how many ceramics are used, what "half-piece" ceramics mean, and specify their polarization directions.

Response: The explanation that " Two half-piece piezoelectric ceramic plates are spliced into one plate according to the opposite polarity. The polarity of the piezoelectric ceramic plate is shown by the blue arrow in Fig. 2(a) and Fig. 2(b)." has been added to the manuscript. (Lines 217-219)

3. The meanings of the symbols θ and γ are not defined in the text. Please define these parameters and explain their physical significance and why these specific ranges were chosen.

Response: The explanation that " As shown in Fig. 2(a) and Fig. 2(b), θ and γ are the included angles between the vibration direction of point A and the axis of the transducer in bending vibration and longitudinal vibration, respectively. In Fig. 3, θ-γ is set in the range of 60° to 120° in order to keep the included angle between the directions of longitudinal vibration and bending vibration at 60°-90°. The closer the included angle between the directions of longitudinal vibration and bending vibration is to 90°, the smaller the amplitude loss is when the oblique oblate ellipse is turned into a circular trajectory by adjusting the phase difference. When the included angle between the directions of longitudinal vibration and bending vibration is equal to 60°, the amplitude loss is small when the oblique oblate ellipse is turned into a circular trajectory by adjusting the phase difference." has been added to the manuscript. (Lines 237-246)

4. All figures should include clear and complete captions for each subfigure (e.g., Fig. 2(a), Fig. 2(b), etc.) to enhance readability and understanding.

Response: All figures have been revised as required.

5. The criteria used for optimization are not well explained. For instance, why was the frequency range for Type A chosen as 16–22 kHz? Frequencies below 20 kHz are typically not considered ultrasonic. Additionally, the rationale behind selecting a θ–γ range of 60° to 120° should be discussed.

Response: The explanation that " For A-type transducer, in order to make the front end of the horn extend out of the transducer laterally, its horn is longer than that of the 20kHz transducer, so the frequency of the A-type transducer is lower. At the same time, in order to ensure that the transducer has enough stiffness, its horn should not be designed too long, and the horn of A-type transducer can be designed in the range of 16–20 kHz. Although the frequency below 20kHz is not ultrasonic, the vibration cutting effect of vibration close to 20 kHz is similar to that of ultrasonic vibration cutting. According to the impedance matching theory put forward by Jiang et al. [30], the transducer can still obtain 70% of the maximum amplitude when it vibrates within the range of 0.4kHz above and below the optimal resonance frequency. Therefore, the difference between  and  is in the range of 0.8kHz, and 70% of the maximum amplitude can be obtained for both longitudinal vibration and bending vibration. In order to make the amplitude of longitudinal vibration and bending vibration as large as possible, the difference between  and  is in the range of 0.4kHz." has been added to the manuscript. (Lines 280-292)

The explanation that " In Fig. 3, θ-γ is set in the range of 60° to 120° in order to keep the included angle between the directions of longitudinal vibration and bending vibration at 60°-90°. The closer the included angle between the directions of longitudinal vibration and bending vibration is to 90°, the smaller the amplitude loss is when the oblique oblate ellipse is turned into a circular trajectory by adjusting the phase difference. When the included angle between the directions of longitudinal vibration and bending vibration is equal to 60°, the amplitude loss is small when the oblique oblate ellipse is turned into a circular trajectory by adjusting the phase difference." has been added to the manuscript. (Lines 239-246)

6. Please specify the software and modules used for simulation (e.g., ANSYS).

Response: The explanation that " The modal analysis module in Ansys Workbench is used for the finite element simulation." has been added to the manuscript. (Lines 319-320)

7. Stiffness is important for the cutting. Although the paper mentions stiffness, no simulation or quantitative analysis is presented. The authors should include stiffness analysis and discuss what stiffness values are required to meet machining needs.

Response: At present, there is no industry standard for the stiffness of tool holder, so it is difficult to design it by quantitative analysis. When designing the ultrasonic tool holder, we compare it with the conventional tool holder, and ensure that the stiffness of the ultrasonic tool holder is not lower than that of the conventional tool holder from the aspects of section size and overhang of horn. At the same time, the heat treatment process is adopted to improve the stiffness of the ultrasonic tool holder. In the process of cutting, listen to the sound of cutting to judge whether the tool holder is chattering. After cutting, observe whether there are chatter marks on the machined surface to judge whether the tool holder has chatter.

8. For the modal analysis, did the authors fix the flange to simulate the actual vibration scenario?

Response: In the case of fixed flange, we carried out simulation, and found that the fixed flange had little influence on vibration frequency and vibration mode, which was consistent with the debugging of transducer.

9. Since two types of piezoelectric ceramics are used to excite the horn, this configuration should be reflected in the simulation setup. A simple modal analysis may not adequately represent the real vibration behavior under excitation.

Response: Half-piece piezoelectric ceramic plate is obtained by cutting the whole ceramic piece with water jet. The materials of the half-piece piezoelectric ceramic plate and the whole ceramic piece are the same, and their configuration will not affect the vibration behavior of the transducer. The simulation design and the measured results are consistent. Modal analysis is a general method for designing longitudinal-bending elliptical vibration ultrasonic transducers, and no additional consideration is needed, such as harmonic response analysis.

10. The desired vibration mode appears at a relatively high modal order, which suggests it may not be the dominant mode. Please discuss the vibration efficiency and whether the mode can be effectively excited during operation.

Response: The explanation that " The size of the transducer in the second-order bending vibration mode is close to that in the first-order longitudinal vibration mode, so the bending vibration mode adopts the higher-order mode. The modes of longitudinal vibration and bending vibration can be excited in practical use, and the amplitude is twice the amplitude required for UVAC, so the vibration efficiency of the transducer can meet the needs of use." has been added to the manuscript. (Lines 448-453)

11. The authors should describe the applied voltage, signal type, and configuration used for the two types of piezoelectric ceramics during vibration testing.

Response: The explanation that " When debugging, a sinusoidal voltage of 360V is applied to the ultrasonic transducer, and the frequency of the output voltage can be changed by adjusting the output of the ultrasonic power supply." has been added to the manuscript. (Lines 499-501)

12. In Figure 9, the measured amplitudes are significantly higher than those in Figures 11 and 12. This discrepancy is confusing and should be addressed and explained.

Response: The explanation that " Fig. 9 shows the maximum amplitude of the transducer at resonance, and the amplitude commonly used in elliptical vibration ultrasonic machining is 6-8μm from peak to peak. Therefore, the study in Fig. 10, Fig. 11 and Fig. 12 is carried out by adjusting the output of the ultrasonic power supply so that the amplitude of the transducer is 8μm." has been added to the manuscript. (Lines 524-527)

13. Due to the discrepancy between the resonant frequencies of longitudinal and bending vibration, is there any potential for overheating on the horn?

Response: The explanation that " Due to the frequency difference between the longitudinal vibration and the bending vibration, after the frequency matching of the transducer, both the longitudinal vibration and the bending vibration do not work at the resonance frequency with the maximum amplitude. However, due to the small difference and the low amplitude adopted, the transducer does not overheat during processing. During the continuous monitoring for two hours, the resonant frequency, output current and amplitude of the transducer are relatively stable." has been added to the manuscript. (Lines 545-551)

14. In Figure 15, the machining results suggest that ultrasonic vibration may degrade surface quality, even though tool life is improved. Surface roughness should be quantitatively measured and reported.

Response: The explanation that " As shown in Fig. 17, the roughness meets the finishing requirement that Ra is less than 1.6μm. The vibration marks on the machined surface of HEUVC slightly increase the roughness, which can be seen from the roughness value at the initial stage of cut-ting. With the progress of cutting, the effect of HEUVC reducing cutting temperature and cutting force will reduce the deterioration of the machined surface by tools, thus achieving a lower surface roughness than CC. " has been added to the manuscript. (Lines 626-631)

15. Tool life alone is insufficient to demonstrate the benefits of the proposed design. It is recommended that cutting forces be measured and compared across conditions.

Response: The explanation that " HEUVC method can partially open the cutting area in the process of continuous cutting, so that the coolant can enter the cutting area to cool and lubricate the tool and workpiece, reduce the cutting temperature and cutting force, and thus prolong the tool life. As shown in Fig. 15, compared with CC, the main cutting force, axial thrust force and radial thrust force of HEUVC are reduced by 17.96%, 17.25% and 16.24% respec-tively when cutting with A-type transducer. Compared with CC, the main cutting force, axial thrust force and radial thrust force of HEUVC are reduced by 16.95%, 18.93% and 15.36% respectively when cutting with B-type transducer." has been added to the manuscript. (Lines 657-664)

16. Can the author explain why type A has a longer tool life than type B?

Response: The explanation that " The rhombic-type tool is used in A-type transducer, while the ball-end tool is used in B-type transducer. Compared with the rhombic-type tool, the length of the cutting edge in which ball-end tool participates in cutting is increased, which makes the cutting heat relatively dispersed, so the tool life of the ball-end tool is longer than that of the rhombic-type tool. Because the rhombic-type tool used in A-type transducer has short tool life, HEUVC can improve more tool life than CC. In other words, the smaller the base, the higher the improvement." has been added to the manuscript. (Lines 615-621)

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have revised the paper based on the reviewers’ comments. However, there are still some minor issues in the paper. The authors should proofread carefully.

1. Figure 9-12, the units are incorrect characters.
2. What is cutting force unit in Figure 15?
3. In Figure 17, the y axis is incorrect.
4. In Figure 7, the longitudinal vibration looks like a bending vibration. Can the authors explain it?

Author Response

1. Figure 9-12, the units are incorrect characters.

Response: The units in the manuscript has been revised

2. What is cutting force unit in Figure 15?

Response: The unit of cutting force is "N", and the figures in the manuscript have been revised.

3. In Figure 17, the y axis is incorrect.

Response: The figure in the manuscript has been revised.

4. In Figure 7, the longitudinal vibration looks like a bending vibration. Can the authors explain it?

Response: The explanation that " In Fig. 7(a) and Fig. 7(c), it can be clearly seen that the transducer part is vibrating longitudinally, while the longitudinal vibration of the horn deflects in the bending direction of the horn, which is caused by structural asymmetry." has been added to the manuscript. (Lines 406-409)

Author Response File: Author Response.pdf