Discussion on Ball Screw Slide–Roll Ratio and Entrainment Velocity Calculation

Round 1

Reviewer 1 Report

Dear Authors, 

I suggest you add some more information in figure legend in order to understand the figure better. 

If it is possible you can make a 3D view of the Ball Screw Slide. 

Otherwise I am alright with this publication.

Best regards

vijay

Author Response

We greatly appreciate your valuable comments on our manuscript; our response is included as an attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper deals with the kinematics of ball screw mechanisms (BSM) in a simple manner. However, the results reflect some issues related to the influence of centrifugal forces and the ratio of rolling and sliding in BSM.

My objections to this work are as follows:

1. The present model is inspired by Wei and Lin [1], and I do not see many differences in the choice of coordinate systems. In addition, the model in [1] is a complex one, considering the equilibrium of the whole mechanism under the action of a dynamic load. Hence, it is normal to have some differences between the results. In fact, the model proposed by the authors treated the kinematics of a single ball, without collision with neighbouring balls. I advise the authors to present their results by comparison with Wei and Lin [1], without further comments. 
2. The results are somewhat normal because the authors chose a symmetric system, i.e. the geometrical parameters of the bolt and nut trajectories are the same. From this it follows that we have similar sliding to rolling ratios. 
3. Of course, if the rotational speed is small there is not much influence of centrifugal force, the finding is normal and well known from the literature. 
4. It is difficult to follow the pattern, while a list of notations including subscripts and superscripts is missing.
5. Regarding the equation in Eq. (15), it is clear that the authors' model has omitted something, since the ball is free to rotate about all axes (rolling, rotating and gyroscopic motion). Why is the first term null? What does ϒ mean?
6. There is much speculation about the efficiency of the transmission. Different sliding speeds on the ball and nut and on the ball and screw do not lead to such a big influence on efficiency, because the mechanism is usually lubricated and the power loss is not so important. In fact, in order to criticize the previous literature, the authors need to develop a better model. Efficiency is not calculated, so speculation is not allowed while the proposed model did not consider the whole mechanism and its dynamics.
7. Another speculative comment is one referring to the lubricated mechanism. Without a dynamic model of the mechanism and a rheological model taking into account the influence of the lubricant, no speculations are allowed.
8. Finally, I believe that this paper needs to be improved before publication, as the model developed is too simple to account for the complexity of BSMs. The contradiction with the existing literature presenting complete models is a strong point to reject this paper.

Author Response

We greatly appreciate your valuable comments on our manuscript; our response is included as an attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper presents an interesting study, with a right methodology and the manuscript is clear, well organized and structured and the authors have worked exhaustively, taking care of the technical details.

It is opinion of the reviewer that the manuscript is very well but some suggestions could improve the paper:

• The introduction section should be improved, taking into account the more relevant studies on the subject to build a complete scientific framework.
• The acronyms should not be used in the abstract.

For these reasons, the reviewer suggests the manuscript for the publication after minor revisions.

Author Response

We greatly appreciate your valuable comments on our manuscript; our response is included as an attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

I appreciate the great efforts of the authors to explain their assumptions, but rechecking the paper I dee that the authors do not even realize the difference between the gyroscopic motion and spin motion, as they call β as being "gyroscopic angle of the ball’s spinning axis". The spin motion is one executed by the ball around the contact axis, while the direction of the gyroscopic motion is perpendicular to the rolling motion vector (which dictates the β angle as the resultant angular velocity angle of the ball) and to spin motion vector (perpendicular to the contact area of the ball and nut and ball and screw).

I must warn the authors that they are mixing complex simulations, requesting coordinate transformation, with simple assumptions from rolling bearings.

Please check again that all your absolute velocities and relative velocities are expressed in the same coordinate frame. Please mention for each vector also its considered frame. We cannot add or subtract vectors expressed in different frames. Please include this specification in the notations list.

The notation "ωt, ωn, ωb = components of the ball’s spinning relative angular speed along t- n- and b-axis", is assuring me that the authors do not make any difference between the three primary angular speeds of the ball: rolling motion, spin motion, and gyroscopic motion.

Taking into account all my suggestions, I advise the authors to rewrite the entire model. The contact elastic deflections of microns do not influence the sliding speed, but they can be included in the model.

I assure the authors that rejecting this paper at this moment is the best solution, as I think they wouldn't like to see future criticism of their model. 

Author Response

We deeply appreciate your efforts valuable comments on our manuscript; our response is included as an attachment.

Author Response File: Author Response.pdf

Round 3

Reviewer 2 Report

The paper is now very clear and I recommend it for publication since I sincerely believe it could help many scientists clarify past errors in previous references. I would also encourage the authors to develop a new complex model as in reference [1], but a perfect one.