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Dear Editors and Reviewers:Thank you for your letter and the reviewers comments concerning our manuscript entitled “Investigation on feed direction cutting force in ultrasonic vibration assisted grinding of dental ceramics” (ID: JMES-15-0637.R1). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. I have studied comments carefully and have made correction which I hope meet with approval. Revised portion are marked in blue in the paper. The main corrections in the paper and the responds to the reviewers comments are listed as follows:Responds to the reviewers comments:Reviewer 1: 1. Equation 8 cant simplify，the middle formulas is not approximately equal to the back of the formula，The formula can solve by Matlab.Answers: I have try to use Matlab to solve this formula, but the operation result is very complex. It is not conducive to calculate this cutting force model. So I simplified the Equation 8 based on the fifth page of reference (33) (Mathematical model for cutting force in rotary ultrasonic face milling of brittle materials. Int J Adv Manuf Tech 2013; 69: 161-170.). Since R vf, vf has very little influence on the calculation results. So it can be ignored. Then I removed the simplifying process of formulas 9, 10, 11. 2. Equation 9 is wrong, please amend.Answers: According to the reviewers comments, I have revised this equation. I also have checked my paper carefully and corrected these mistakes.3. The vibration amplitude is about 5 m and the vibration frequency varies from 20 to 50 KHz, however, the frequency in test is held constant , f=25kHz, and in Analysis of experimental results, Fig.9 (f) (g), Amplitude and frequency is variable. These data are inconsistent.Answers: The influences of ultrasonic amplitude and frequency on cutting force cannot be ignored. Considering the rationality and applicability of this model, amplitude and frequency must be set to variable in the process of developing cutting force model. However, in the specific experiment, ultrasonic frequency is affected by many factors, especially for extended length of tool, size and material of workpiece. Through adjust the frequency value during experiment, we found that only when f = 25 KHz (corresponding amplitude is 5m), the effect of ultrasonic vibration is more obvious. Therefore, we selected frequency and amplitude as constant in experiment.Special thanks to you for your good comments.Comment 1: Please pay attention to the figure numbers in this paper. For example, in the fourth page, “During UVAG, motion of single lateral abrasive particle is a combination of three motions (e.g., axial ultrasonic vibration, spindle rotation, and horizontal feeding), as illustrated in Fig. 1a”, Fig. 1a should be changed to Fig.3a here?Answers: The purpose of Fig.3 is to illustrate the two models that abrasive particles take part in cutting under the different input value of cutting depth ap. And in this paper, the main consideration is the model shown in Fig.3a. Fig. 1 expresses the form of ultrasonic machining, feeding and rotation direction of the tool, and direction of the ultrasonic vibration. Eq. (3) (4) is obtained according to the Fig. 1.Comment 2:There are some incorrect expressions in this paper. For example, in the fourth page, “Cutting process of lateral abrasive particles is different from abrasive particles on the end during UVAG”, I do not quite understand what it means.Answers: I am very sorry for these errors. And I have tried my best to revise our manuscript. Besides, the people who have a high level of English helped me revise my manuscript.Comment 3: In the fifth page, The Eq. (9) should be an issue.Answers: I have revised this equation. I also have checked my paper carefully and corrected these mistakes.Comment 4:There are some problems in derivation and simplified process of Eq. (11), Eq. (13) and Eq. (15) in the fifth and sixth pages. Please do some necessary instructions!Answers: According to reviewers comments, I simplified the Equation 8 based on the fifth page of reference (33) and removed the simplifying process of formulas 9, 10, 11 in the original paper and readjusted the number of all formulas in this paper. Eq. (13) becomes Eq. (11) and Eq. (15) becomes Eq. (13) in the revised paper.The Eq. (13) is not simplified. I made mistakes in the process of writing. I have corrected this formula. The Eq. (15) is calculated as follows: Comment 5: “The predicted relationship between cutting force and input variables (spindle speed, feed rate, cutting depth, abrasive concentration, abrasive size, semi-angle of abrasive particle, ultrasonic vibration amplitude and frequency) are shown in Fig.10”. But the pilot experiments of model only takes into account part of these parameters. Why?Answers: UVAG experiments are carried out at a DMG Ultrasonic 20 Linear high speed machining center. The ultrasonic frequency is a resonant frequency. It is affected by many factors in the specific experiment, especially for extended length of tool, size and material of workpiece. The tool and workpiece are determined during the experiment. Through adjust the frequency value before experiment, we found that only when f = 25 KHz (corresponding amplitude is 5m), the effect of ultrasonic vibration is more obvious. In other frequencies, it very easily leads resonance in other directions, and this situation will cause serious damage to the machine and tool. Therefore, we selected frequency and amplitude as constant in experiment. However, the influences of ultrasonic amplitude and frequency on cutting force cannot be ignored. Hence, considering the rationality and applicability of this model, amplitude and frequency must be set to variable in the process of developing cutting force model.The tool used in DMG Ultrasonic 20 Linear high speed machining center is special cutting tool. Based on the existing exper