Review Reports - Study of the Vibration Isolation Properties of a Pneumatic Suspension System for the Seat of a Working Machine with Adjustable Stiffness

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper proposes a topic of current interest. However, there different issues to be addressed by the authors:

1) In the introduction section, the authors should also remember that metal devices [A,B] may be adopted as passive control devices.

[A] https://doi.org/10.1016/j.matdes.2022.111436

[B] https://doi.org/10.1007/978-3-030-34713-0_31

2) The title of Section 1.1 is too much long. Please, shorten it.

3) The title of Section 2 is not a title. Please, reformulate properly it. In addition, please, note that section 2.2 has the same “title” of section 2.

4) Please, shorten section 1.1 since it is too much long.

5) Check Equation (9).

6) The paper need to be re-organized since there are only 2 main sections. Section 2 may be divided into two different sections.

7) Please, better underline, in the last part of the manuscript, the advantages of the proposed vibration control solution with respect the conventional ones.

Comments on the Quality of English Language

None

Author Response

Dear Reviewer,

Thank you for your valuable comments. We agree with these comments. We also refer to specific points:

Comments 1: In the introduction section, the authors should also remember that metal devices [A,B] may be adopted as passive control devices.

Response 1: Thank you for your literature suggestions. The latest literature item in biliography has been added.

Comments 2: The title of Section 1.1 is too much long. Please, shorten it.

Response 2: The content of section 1 has been reworded into a shorter version

Comments 3: The title of Section 2 is not a title. Please, reformulate properly it. In addition, please, note that section 2.2 has the same “title” of section 2.

Response 3: Thank you for your valuable comment. The structure of the document has been thoroughly rewritten taking into account your suggestions. The titles of the various sections have been changed and some sections have been deleted.

Comments 4: Please, shorten section 1.1 since it is too much long.

Response 4: Section 1.1 is now shorter. In addition, Section 1 has been divided into subsections 1.1 and 1.2. After your suggestions and those of the other reviewers, the structure of the document has been significantly changed.

Comments 5: Check Equation (9).

Response 5: Equation 9 has been re-checked. In order to determine the derivative dp/dh occurring in equation 8 after differentiating the adiabatic transformation, this relationship is obtained.

Comments 6: The paper need to be re-organized since there are only 2 main sections. Section 2 may be divided into two different sections.

Response 6: The paper has been extensively restructured as to the division into different sections:

The division now looks like this:

Introduction

1.1. Suspension types of vehicle driver seats

1.2. Functionality of semi-active suspension systems

Test stand description
Physical and mathematical model of a single-degree-of-freedom seat suspension

3.1. Results of the theoretical and experimental analysis

Air-spring equation
Experimental and modelling studies of the harmonic motion

Conclusions

Comments 7: Please, better underline, in the last part of the manuscript, the advantages of the proposed vibration control solution with respect the conventional ones.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Here are some points which are not clear and should be improved

line 249 -> unit of force kG - usage of SI Unit "N" more common

equation (4): h -> daming exponent is often decribt with \delta

equation (9): badly scaled in vertical direction ( equations 9-15 are all scaled different?)

fihure (14): the legend outside the diagram would be better

line 507: eigenform or mode shape instead of forms

figure (3)+(16): bad resoultion

Tabela 4. -> table 4? -> 7 digits of the position yf and fc -> 4 are sufficent in this context

figure (8a) : "xperimental" -> experimental int the legend

To measure a frequency response with a good frequency resolution a noise signal excitation and a long signal length are usefull. In the paper the time signal from equation (5 ) is used to excite the system. This is maybe not good to excite all frequencies of the system. On the other hand, the differential equation can be used to calculate an analytical solution for the frequency response.

line 603: mf -> "mass" of the seat

line 604: g -> acceleration of gravity [PHYS.]

line 605: Aw -> excitation amplitude

Comments on the Quality of English Language

Some physical and mechanical terminology is incorrect.

Author Response

Dear Reviewer,

Thank you for your valuable comments. We agree with these comments. We also refer to specific points:

Comments 1: line 249 -> unit of force kG - usage of SI Unit "N" more common

Response 1 : Thank you for pointing this out. Revised according to the recommendation.

Comments 2: equation (4): h ->daming exponent is often decribt with \delta

Response 2: Thank you very much for your suggestions. The coefficient h is called the normalized damping factor. For this coefficient, various designations are used in bibliography. For the purpose of this study, one of the designations used in bibliography - h - has been adopted. Corrected with the reviewer's suggestions.

Comments 3: equation (9): badly scaled in vertical direction ( equations 9-15 are all scaled different?)

Response 3 : Thank you for your attention. Pattern scaling has been corrected.

Comments 4: fihure (14): the legend outside the diagram would be better

Response 4: The layout of the legend in the drawing has been changed.

Comments 5: line 507: eigenform or mode shape instead of forms

Response 5: The text was changed according to the orders.

Comments 6: figure (3)+(16): bad resolution.

Response 6: The quality (resolution) of defective drawings has been improved.

Comments 7: Tabela 4. -> table 4? -> 7 digits of the position yf and fc -> 4 are sufficent in this context

Response 7: Corrected with the reviewer's suggestions.

Comments 8: figure (8a) : "xperimental" -> experimental int the legend

Response 8 : The description of the drawing has been corrected.

Comments 9: To measure a frequency response with a good frequency resolution a noise signal excitation and a long signal length are usefull. In the paper the time signal from equation (5 ) is used to excite the system. This is maybe not good to excite all frequencies of the system. On the other hand, the differential equation can be used to calculate an analytical solution for the frequency response.

Response 9: Thank you for your valuable comment. The model of the forcing acting on the seat suspension base corresponds with sufficient accuracy to the course of the variation of the forcing set during the experimental tests. The responses of the system to the preset forcing obtained during numerical simulation correspond with sufficient accuracy to the responses of the real system. The applied shape of the forcing significantly affects comfort in the operator's work and is not susceptible to passive vibration. We agree with the reviewer's suggestions, however, we would like to point out that the use of active control of the system's response to a given forcing requires an apparatus that processes a fast-variable process. Any excessive delay can lead to low effectiveness of the applied vibration isolation. Therefore, the presented shape of the forcing was chosen for analysis.

Comments 10: line 603: mf -> "mass" of the seat

Response 10: Changed as recommended.

Comments 11: line 604: g -> acceleration of gravity [PHYS.]

Response 11: Changed as recommended.

Comments 12: line 605: Aw -> excitation amplitude

Response 12: Changed as recommended.

Thanks again for your valuable comments.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Please see attached file.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

In terms of style, much of the language is overwrought. It’s better to write simply and directly.

Part of the confusion in the simulation method (as described in the Comments and suggestions for authors) could arise from use of the obscuring phrase, “the course of the variation of _________ as a function of ________ .” Showing the dependence of one variable upon another is clear, but it’s critical to discuss why the dependence or functionality is as it appears. Rewrite all passages where this appears, and describe simply and explicitly what is presented.

In line 297, the model should be “Voigt-Kelvin.”

In line 300, the citation and reference to the Rakhej source is missing.

In line 321, “gdzie” should be translated.

In line 342, change it to Figure 5.

Line 378 includes a mention of “seat mass with a human subject,” however, there is no human subject in this work.

In lines 439, 445, and 456, variables should be defined with the words “is the” rather than an em-dash. That is, “…where: h is the bellows deflection…”

Line 558 has a hyphenated “passive.”

In eq. (10) following line 450, a new variable p_s is introduced but not defined.

The legends and axes labels for several plots do not use consistent variable names. For example, Figures 11 and 12 have y_bisf1 and Figure 15 has “Ksp” rather than k_s. All figures should be checked and corrected for consistent variable names.

In the Conclusion, a couple of phrases are used inaccurately. Line 580 has “scattering properties,” and line 581 uses “restitution properties.” By scattering properties, perhaps the authors are referring to the effective stiffness and damping as a function of air bellows pressure? It’s not clear at all what restitution properties would be. That term is defined in mechanics in a specific case of a body experiencing a collision, and the restitution coefficient is the ratio of the velocity after the collision to that prior to the collision.

Reference 9 is missing the title of the proceedings. The complete citation should be:

Yue Bian, Yitong Wang, Mingming Dong, and Han Kong "Research on vertical vibration characteristics of human body under standard sitting posture", Proc. SPIE 12612, International Conference on Artificial Intelligence and Industrial Design (AIID 2022), 126121B (14 April 2023); https://doi.org/10.1117/12.2673028

Author Response

Dear Reviewer,

Thank you for your valuable comments.We agree with these comments. We also refer to specific points:

Comments on the Quality of English Language:

Comments 1: In terms of style, much of the language is overwrought. It’s better to write simply and directly.

Response 1 : Thank you for your suggestions. We are aware of its imperfections. However, an attempt has been made in the paper to convey information in an accessible manner with a logical interpretation of the research methodology used and the results obtained. We believe that the language used in most of the paper should be understandable to most readers.

Comments 2: Part of the confusion in the simulation method (as described in the Comments and suggestions for authors) could arise from use of the obscuring phrase, “the course of the variation of _________ as a function of ________ .” Showing the dependence of one variable upon another is clear, but it’s critical to discuss why the dependence or functionality is as it appears. Rewrite all passages where this appears, and describe simply and explicitly what is presented.

Response 2: The use of the expression "the course of variation “ is a formula used in mathematics and mechanics to describe the relationship between physical quantities. We will include a comment on the broader interpretation of the relationships obtained.

Comments 3-10: In line 297, the model should be “Voigt-Kelvin.”, In line 321, “gdzie” should be translated., In line 342, change it to Figure 5., Line 378 includes a mention of “seat mass with a human subject,” however, there is no human subject in this work., Line 558 has a hyphenated “passive.”., In eq. (10) following line 450, a new variable ps is introduced but not defined., The legends and axes labels for several plots do not use consistent variable names. For example, Figures 11 and 12 have ybisf1 and Figure 15 has “Ksp” rather than ks. All figures should be checked and corrected for consistent variable names., In lines 439, 445, and 456, variables should be defined with the words “is the” rather than an em-dash. That is, “…where: h is the bellows deflection…”, In the Conclusion, a couple of phrases are used inaccurately. Line 580 has “scattering properties,” and line 581 uses “restitution properties.” By scattering properties, perhaps the authors are referring to the effective stiffness and damping as a function of air bellows pressure? It’s not clear at all what restitution properties would be. That term is defined in mechanics in a specific case of a body experiencing a collision, and the restitution coefficient is the ratio of the velocity after the collision to that prior to the collision.

Response 3 -10: Thank you for your valuable editorial comments. All suggestions have been implemented and corrected in the paper.

Comments 11: In line 300, the citation and reference to the Rakhej source is missing,

Response 11: A literature item was added and cited.

Comments 12:Reference 9 is missing the title of the proceedings. The complete citation should be: Yue Bian, Yitong Wang, Mingming Dong, and Han Kong "Research on vertical vibration characteristics of human body under standard sitting posture", Proc. SPIE 12612, International Conference on Artificial Intelligence and Industrial Design (AIID 2022), 126121B (14 April 2023); https://doi.org/10.1117/12.2673028

Response 12: Corrected according to your suggestion.

Comments and Suggestions for Authors

Comments 1: The Introduction section is an accessible overview of the topic, but the connections to the substance of the paper is weak. This could be strengthened if the case were clearly made that the pneumatic suspension design is a semi-active isolation mechanism. More discussion of the stiffness and damping characteristics of the air bellows, right at the start of the manuscript, would help to make this case. Also missing from the Introduction is any mention of transmissibility. More on thatisnotedbelow.

Response 1: A description has been added to the introduction, referring to the main focus of the article, which is research on the pneumatic bellows

Comments 2: The air bellows unit is really the star of the show, but aside from its dimensions, we know little about it. Ist here a manufacturer and model number?

Response 2: Section 3 was supplemented with an available description of the manufacturer and use of the air bellows. A diagram of the bellows used has been added to Figure 2.

Comments 3: The variable called y in the manuscript is not clearly defined. Figure 2 defines y as the position of the seat, the top member of the scissor jack structure, with a positive upward. Two aspects of the results (e. g., Figure 5, mislabeled in the manuscript as a second Figure 4) are of concern:

a) The table (lower part of the scissor) is moved upward by 63 mm, and the value of y immediately goes NEGATIVE by 63 mm. Shouldn’t the seat also move upward? Perhaps the sign of the laser data is backward?
b) The seat position oscillates after the step function, which damps out and returns to zero. Shouldn’t it oscillate around its new position 63 mm higher than before the step function input? Instead, it oscillates around zero, indicating this y is NOT position, but displacement… but, displacement from what reference position? These concerns lead to the next item and may be resolved with a clear revision.

Response 3 : The y-coordinate indicates the vertical displacement of the inertial element..

The designation of Figures 4 and 5 has been changed.

There are incorrect markings in Figures 5 to 8. Obviously, when forced by the function given in Figure 4, the mass m moves vertically upwards. Figures 5 and 7 show relative displacements, hence the negative values in the diagrams. The designations in the figures have been corrected.
The motion of the mass m is assumed to be around the static equilibrium position. The static displacement of the inertial element is included in Equation 2. Therefore, after the removal of the force, the system tries to return to the static equilibrium position. In the numerical simulation process for the formulated model, the system always returns to the static equilibrium position. In contrast, for the real system, there may be deviations because the bellows are not completely stable. The parameterisation of the model has also taken into account the possibility of deviations. To compare the results obtained from the numerical simulation with those obtained from the experimental tests, the response of the real system is also given taking into account the static equilibrium position.

Comments 4: The description of the method for the experiment as well as the simulation is not clear. Reorganizing the presentation of this work could clarify both. The traditional sections of a scientific work are recommended: following the Introduction, present the Theory (encompassing the 1-DOF model and its known parameters, plus the parameters that would necessarily depend on selected experimental results), carefully describe the Experiment Method and Results, use a Discussion section to explain how some of the experimental measurements feed into the simulation, and how the implementation of an optimization algorithm could be constructed, and finally tie it all together with a short Conclusion. As written, the logical flow bounces between simulation and experiment, with many details left out. A few examples:

a) What is the excitation provided by the pneumatic cylinder, and why was it set to be the way it is? (Actually, there were two excitations explored here: the double-step function up and down and the sinusoidal tests.)
b) Regarding the experiment design, the air bellows is mounted to the midpoint of the scissor structure, not the vibrating floor as claimed. The midpoint will have its own displacement that is different than that of the floor, or that of the seat, though there may be some proportionality to the relative difference between the two. How is this ignorable in the model?
c) How were model stiffness and damping set? Why would they change as a function of time? (Section 2.3 has some of this, but it doesn’t fully explain the simulation choices.) Figures 9 and 10 seemed to come out of the blue. Were the stiffness, damping, and static displacement all adjusted for best fit to experimental data (in order to yield Figures 5 and 7)?
d) The definition of yf1st in line 313 is unclear… this is static displacement of the entire system due to mass loading; if the mass and stiffness are known, should this not depend on the two? Referring to the previous question c) above, is the static displacement in Figure 10(b) a free parameter, or is it determined by mass and stiffness?
e) Frequency of free vibration is predicted from the model. Is that seen in the ringing of the displacement variables? Or, in the spectral presentation (i.e., Figures 6 and 8)?
f) There’s no discussion of the spectra in Figures 6 and 8. What value do they bring to the story you’re telling?
g) Figure 10 incorporates two additional mass values, which are not defined until further below, in the caption for Figure 11. What is the intention here? If that is explained more clearly a priori, in a section on the simulation method, this wouldn’t be a surprise to the reader. In the current manuscript, it’s only clear when we get to line 400 or so, as we’re considering an implementation procedure for optimizing the suspension for a given operator.
h) Table 2 includes the “standard deviation of the variation of displacement as a function of time.” This could be interpreted in different ways. The simplest might be to find the standard deviation of all the values of y collected during the experiment. But, this doesn’t make sense because the spread in the data will most strongly depend on the thrust of the table (63 mm). Alternatively, it could be the standard deviation of the difference (y – yf1). That would provide a measure of the spread of the variation between the data and the simulation. Or, because the displacement in the figures seems to be relative to some expected position of the seat, it would be ideally zero…? Clear definitions for each variable in the measurement and analysis are lacking.
i) The driving frequency used to produce results in Figures 21 and 22 is not given, unless I missed it somewhere.
j) Are the terms “passive soft,” “passive optimum,” and “passive hard” derived from a source in the literature, or defined specifically for this work? It’s not clear what the criteria are, or how that relates to the hypothetical ideal range of amplitude gain, 0.3 to 0.7. And, why not shoot for 0.1? (What makes that ideal range ideal?)
k) The frequency response to the chirped (modulated) driving signal is given in Figure 23(b). Is that the amplitude gain, y/y0, expressed in dB, relative to 1? Or is it simply 20 log10 (y)? It would be more helpful if it were the amplitude gain in dB. That approaches the concept of transmissibility.

Response 4: Thank you for your comments on the structure of the paper and how to improve its readability. The structure of the paper has been revised. A physical model of the test rig was formulated before developing a programme to simulate the motion of the system. The main emphasis in the development of the physical model was on its simple structure, which nevertheless allows results that differ little from those obtained experimentally. The emphasis was on determining the elastic properties of the system by determining changes in the stiffness coefficient. Its estimation depends on the experimental results obtained. The inertial parameters resulting from the man-seat system were taken from the work of S. Rakhej. The form of the constraint was chosen so as not to have a significant negative effect on the comfort of the operator's work and not to be susceptible to passive vibrations. The use of active control, on the other hand, would have presented difficulties due to the presence of a rapidly changing process. Excessive delays could lead to poor effectiveness of the applied vibration isolation. Taking into account the above assumptions, the forcing shown in Figure 4 was chosen for the analysis. The shape of the developed forcing model differs slightly from the real forcing obtained during the experimental tests. The responses of the system to the given forcing obtained during the numerical simulation correspond to the responses of the real system with sufficient accuracy. Therefore, it can be assumed that the behaviour of the virtual model corresponds to the real system. The construction of an optimisation algorithm for a selected class of forcings is a difficult problem and requires further research. We plan to develop an implementation of the optimisation algorithm taking into account the results of the work carried out, which are included in this article. At this stage of the work, we have found that two possible optimisation criteria lead to the assumption of completely different values of the bellows pressure for a given mass of the inertial element. This conclusion follows from the interpretation of the relationships shown in Fig.11 and Fig.12. Consequently, it is difficult to determine the optimum value of the initial pressure in the bellows for the comfort of an operator with a given mass.

a) The shape of the forcing has been chosen so as not to have a significant negative impact on operator comfort and not to be susceptible to passive vibration isolation, whereas the use of active control would present difficulties due to the presence of a fast-moving process. The excessive delays that would occur could lead to poor effectiveness of the vibration isolation applied. Given the above assumptions, the forcing shown in Figure 4 was selected for analysis. The shape of the developed forcing model differs only slightly from the actual forcing obtained during experimental tests. Sinusoidal tests are the simplest form of analysing the system for external forcing. They are used in this study to confirm the correct choice of model and its parameterisation. This means that it is a type of test to verify the correctness of the test method used.

b) One of the assumptions in accepting the virtual model for consideration was its simple structure. Therefore, it was not necessary to map the suspension geometry of the bellows seat. A condition for dispensing with calculations taking into account the peculiarities of the suspension geometry was that the responses of the model and the real system should not differ significantly. The bellows itself is an object whose parameters can be approximated. Consequently, the elaboration of relationships derived from the suspension geometry does not necessarily lead to more accurate results. Simulating the movement of a more complex model may lead to greater errors. This needs to be checked and we intend to take this into account in further stages of the work.

(c) From equation (15), taking into account the characteristics of the bellows, it follows that the stiffness of the bellows is a function of two arguments whose values change with time. Both the pressure and the deformation of the bellows are functions of time, so the stiffness of the bellows must vary as a function of time. Based on this assumption, runs of stiffness variation as a function of pressure have been developed for moments in time that are important in shaping the response of the system to a given forcing. In this way, it is possible to determine the stiffness versus time curve for any value of pressure. Changing the value of damping as a function of time also reduces the response error of the model relative to the response of the real system to a given forcing. The static displacement is derived from the output stiffness values for the bellows provided by the manufacturer as a function of pressure. This allows the static displacement value to be determined as a function of pressure for a given mass of the inertial element.

d) The static displacement determined from equation (3) depends on both stiffness and mass values. It is therefore determined by both stiffness and mass. This is discussed in more detail in (c).

e), f) The free vibration frequency is relevant for forcing with a similar frequency band. For the adopted forcing model, it is difficult to determine the influence of this frequency on the displacement variation waveform. To compare how the system processes displacement signals of different frequencies for the simulation experiment with the real one, frequency characteristics are presented (Figures 6 and 8). The data obtained allows the graphs to be analysed in terms of amplitude variation as a function of frequency. The logarithmic characteristics, on the other hand, highlight changes in the stop band (1-15 Hz) where the signal amplitude is significantly attenuated.

g) The introduction of additional mass values is very important to ensure operator comfort with a certain weight. The objective of considerations already carried out and planned is the possibility of automatically selecting the initial value of the bellows pressure depending on the weight of the operator. Ultimately, consideration is being given to the possibility of automatically measuring the weight of the operator sitting on the seat and, on this basis, having the installed system set the most favourable pressure value. Additional clarification has been introduced in the simulation method section.

h) A correction has been made in the table. Table 2 shows the standard deviation of the relative displacement δ_(y_f1-y_f0 )for selected values of the initial bellows pressure. This provides estimates that enable the response of the real system to be compared with the responses obtained by simulating the movement of the model for a given forcing. Two criteria have been introduced based on which operator comfort and safety can be assessed. These are the effective acceleration y ̈_f1RMS and the maximum relative displacement (y_f1-y_f0 )_max as in Figure 11. These are opposing criteria for the quality of vibration isolation. It is therefore necessary to decide which parameter we consider more important. Acceleration can directly affect a person's internal organs and displacement can affect the perception of the activities performed. Therefore, obtaining a zero standard deviation value does not necessarily imply a perfect solution. The quantities occurring in the model analysis are discussed in detail in Chapter 3 (these are y_f1 and y_f0), while those occurring in the measurement are discussed in Chapter 2 (these are y and y_0). Only those quantities required to calculate the standard deviation of relative displacement are listed here.
i) The frequency is the same. The drawings were scaled, wrong on the time scale.

j) The problem of selecting the correct 'type of damping' is a complex process because the vibration isolation criteria are opposite, that is, with the theoretical value of the absolute acceleration of the mass equal to zero, the amplitude of the relative displacement is equal to the amplitude of the forcing. Such vibration isolation in the case of work machine operator seats is not desirable because the feet of the work machine operator perform movements in the vertical direction with amplitude values equal to the floor forcing. When the isolated mass performs movements in line with the forcing, its absolute acceleration value is equal to the acceleration of the forcing. Most currently developed active seat suspension systems operate according to the 'Sky-Hook Damper' algorithm, having feedback proportional to the value of the absolute velocity of the isolated mass. This technical solution exposes the operator to excessive movement of his or her legs and, as a result, worsens the health of the hip joints. Also, the operator's control over the working machine is reduced due to the large vertical displacements of its controls, rigidly attached to the body of the machine. Another important negative effect of large maximum relative displacements is contact with the end bumpers of the suspension system. By contractually setting a range for the amplitude amplification factor, we are attempting to reconcile these two opposing criteria for acceleration and relative displacement of the seat operator (Figure 12). Determining the 'optimum damping' is a kind of compromise between these criteria.

k) This is explained in point e). We agree that it can be represented in different ways. Magnitude is often used in the context of spectral analysis of signals, where it shows how the energy of a signal is distributed at different frequencies. It is a measure to determine how strong a signal is at a given frequency.

Comments 5: Section 2.2 begins with an extended biomechanical description in a paragraph some 60 lines long (specifically, 221 – 288). None of this has any relevance to the objective stated in the header because, in the model, the body (and seat, in the 1-DOF model) is taken to be a lump of mass. The whole paragraph could be deleted with no impact on the message of the manuscript.

Response 5: The comment has been taken into account. Reduced t and left only the necessary information that illustrates the need for the research presented in the article.

Comments 6: Section 2.3 appears quite reasonable in its discussion of the theoretical dependence of the air bellows stiffness on pressure, Eq. (15). It also provides a (measured?) pressure as a function of time for the stepfunction tests, in Figure 14. This would have been very helpful to the reader if presented earlier (say, in the Theory section outlining the simulation method). Even more helpful, how do the results presented in Figure 15 correlate to the values used in Figure 9?

Response 6: Thus, Figure 14 shows the bench-measured pressure variation waveforms as a function of time for selected initial bellows pressures. We believe that the presentation of this figure in both Chapter 3 and Chapter 4 is justified. We have chosen Chapter 4. In Figure 14, two characteristic time instants can be observed, i.e. for t≈0.5 [s] and t≈2 [s]. A clear increase in the bellows pressure can be seen. This corresponds to moments of increasing forcing and decreasing forcing, as in Figure 4. This is a rapidly varying process. Nevertheless, the obtained waveforms of relative displacement variation as a function of time for both the experimental tests and the numerical simulation show clear changes in values at these moments, as in Figures 5 and 7. The increase in pressure values at the moments considered to be characteristic translates into a change in the value of the suspension rigidity of the seat, as in Figure 9. This conclusion is reached after carrying out the numerical simulation and comparing the results obtained in this way with the results obtained from measurements made on the test bench.

Comments 7: Section 2.4 is a nice extension of the 1-DOF model, but it’s not clear that it adds any value. It includes unstated assumptions, like continuous contact between the seat and the operator’s body, and value for parameters are unexplained as well (stiffness of 70 kN/m?). The paragraph following the simulation results with a 2-DOF model, lines 540-546, provides no interpretation or application of the results. In fact, that paragraph might be more appropriate as a lead-in to start a new section. The 2-DOF model doesn’t contribute to the overall message of the work. It might be presented as an appendix.

Response 7: This chapter presents a virtual model with two degrees of freedom. I have moved this chapter to the end of the article and as an appendix. The simulations show that the inclusion of a seat cushion in the model can have a significant impact on operator comfort and safety. A cushion stiffness of 70 kN/m and a damping of 150 Ns/m were assumed in the considerations. These are the susceptibility values of a sponge seat cushion. It is possible to use a cushion made of a different material and then the compliance values will be different. The results obtained indicate that the use of an additional passive vibration isolation element in the form of a cushion can have a significant effect on the excitation acting on the operator. However, this requires additional analysis and verification of the vibration isolation criteria for cushions made of several different materials. Determining the optimum susceptibility parameters for the cushion may prove to be very important. The results obtained from the analysis of the two-degree-of-freedom system indicate a clear direction for further research.

Comments 8: A new section should begin with line 547 (or perhaps 540), maybe section 2.5? In a proper revision, this would be a second experiment with a second type of excitation. Here, the concept of transmissibility can really be explored, with vibration isolation as a function of frequency. Figures 21 and 22 present results at only one driving frequency, but in terms of transmissibility, the dependence of stiffness (and damping?) on air bellows pressure allow us to see both isolation as well as amplification. The chirp or modulated driving frequency is 1-5 Hz, but this does not cover the range of concern laid out in the Introduction, lines 130-132.

Response 8: The range of frequencies considered includes the influence of external excitations with a frequency band corresponding to the excitation of parts of the human internal organs. The considerations presented in this chapter are, on the one hand, a form of test to verify the applied methodology for the determination of seat suspension parameters, and on the other hand, they enable the vibration isolation coefficient to be determined at harmonic excitations for different values of the initial pressure in the bellows (Table 3). The results obtained from the simulations (Figure 17) were compared with the results obtained through bench measurements (Figure 16). In this way, a validation of the theoretical model was carried out. The results obtained can be used to further investigate the behaviour of the system subjected to harmonic forcing. Particularly important are the studies resulting from the action of excitations in the higher frequency band, which hurt the head and eyesight.

Comments 9: There is a difference between optimizing an air-bellows suspension design for each operator and a semi-active suspension that adapts continuously to changing conditions or desired responses. The current work describes the former, and it has merit on its own. However, the extended description in the Introduction is more concerned with the latter, and the claims in the Conclusion are only weakly tied to the results of the simulation and tests. These connections can be made stronger with specific interpretation in a Discussion section.

Response 9: Optimising the suspension of the air bellows operator seat is very important to ensure operator comfort and safety. We have discussed this problem more extensively in sections 4h and 4j of the answers to the questions. Two criteria have been introduced against which operator comfort and safety can be assessed. These are the effective acceleration y ̈_f1RMS and the maximum value of the relative displacement (y_f1-y_f0 )_max as in Figure 11. These are opposite criteria for the quality of vibration isolation. Section 3.1 extensively discusses the results obtained and the methodology of how the system automatically selects the initial value of the bellows pressure depending on the current weight of the operator sitting on the seat. Particular attention was paid to the determination of passive vibration isolation parameters. For excitations generating higher frequency bands, active vibration isolation should be used.

Comments 10: Also in the Conclusion, the aim is described as “isolating the person on the seat from external disturbances…” It’s not used in this paper, but the concept of transmissibility should used in the analysis of the results. It may conventionally be cast as a force ratio, of output over input, but it could be reasonably defined here as the displacement (either y or yf1) over table displacement y0. In one spot, around line 549, this idea is approached but never really realized.

Response 10: We wrote about the advisability of carrying out both experimental and theoretical studies of the forcing in the form of a harmonic function in section 8 of the question. The dependence of the vibration isolation coefficient on the selected values of the initial pressure in the bellows is shown in Table 3. The vibration isolation coefficients determined during the experimental research and theoretical analysis are the coefficients K_u=y/y_0 and K_uf=y_f1/y_f0. We have already written about the need for further research in this area in previous answers to the question.

Thanks again for your valuable comments.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors addressed all the issues thus the paper can be accepted.

Author Response

Thank you for your work and your valuable comments.

Reviewer 3 Report

Comments and Suggestions for Authors

The reorganization and renumbering of sections of the manuscript is a marked improvement. The added details and interpretive explanations are also helpful. Only a few suggestions:

Line 275ff. It’s enormously helpful to have displacement defined carefully in Fig. 5 and others. However, in the definition of the model, it’s still not clear that yf1 is a position (displacement from an absolute zero)… or is it a displacement relative to the static displacement, or a displacement relative to some other location/reference? This is not a critique of the model or substance, but a request for clear communication of the work.

Line 475. This would be the place to identify the frequency of the forcing function. “…with a maximum amplitude of y0 = 63 mm and frequency of ______.” This was requested in the review of the first version, and the author reply was “The frequency is the same.” Observing the zero crossings in Figure 16, it’s clear that the graph in (d) has a higher frequency than the others. Figure 17 has observably more variation in the driving frequency, based on the number of periods one may count within a second. It’s not clear what is going on here.

Line 490ff. The original review asked whether the graph in Figure 18(b) shows the magnitude in dB for amplitude or amplitude ratio (called Ku here). It’s strongly suggested to use the latter, 20 log10 (Ku). The problem is that the driving actuator has its own frequency response, less amplitude at higher frequencies, so naturally one might expect the displacement to also decrease at higher frequencies. To effectively make the point in line 493-494 that the system reduces vibration more effectively at some frequencies than others, you should normalize or divide by the driving amplitude.

Comments on the Quality of English Language

The language used is not incorrect or inaccurate, but the quality of communication is still low. More words are used than are needed, but the authors replied with the observation that the language should be understandable. That is true.

Take, for example, the introductory paragraphs of the new section 3 (lines 227-257). The point of these paragraphs is to establish that machinery and vehicles have human operators, who assess conditions, execute responses, and perform actions. None of these factors are incorporated in the single degree of freedom described in section 3. It’s all rendered moot in the next paragraph (around line 261). Readers of this journal are aware that the human anatomy is complex, so all that is needed is to say “the human anthropo-dynamic model has been reduced to a concentrated mass…” Still, this is reduced from the first version, so we may proceed onwards.

Author Response

Dear Reviewer,

Thank you for your valuable comments.We agree with these comments. We also refer to specific sugestion:

Comments 1: Line 275ff. It’s enormously helpful to have displacement defined carefully in Fig. 5 and others. However, in the definition of the model, it’s still not clear that yf1 is a position (displacement from an absolute zero)… or is it a displacement relative to the static displacement, or a displacement relative to some other location/reference? This is not a critique of the model or substance, but a request for clear communication of the work.

Response 1: Equation (2) is the mathematical model describing the motion of the physical system shown in Figure 3. In this equation, there is a component mg on the right-hand side representing the weight of the passive deformable element in the form of a Voigt-Kelvin rheological model. Consequently, the static displacement of the mass m, obtained from the equilibrium equation (3), must be included in the equation of motion (2). Without the component in equation (2), the system model would be excited to oscillate even before the introduction of the force. The mass m is placed on the seat during the experimental tests and does not move. Only introducing an external force, in the model these are the components and causes the system to move. Therefore is the displacement of the mass m relative to the static displacement .

Comments 2: Line 475. This would be the place to identify the frequency of the forcing function. “…with a maximum amplitude of y0 = 63 mm and frequency of ______.” This was requested in the review of the first version, and the author reply was “The frequency is the same.” Observing the zero crossings in Figure 16, it’s clear that the graph in (d) has a higher frequency than the others. Figure 17 has observably more variation in the driving frequency, based on the number of periods one may count within a second. It’s not clear what is going on here.

Response 2 : Thank you for identifying this error and we apologise for any inconvenience caused. In figures 16 a), b) and c) the forcing frequency is 20 [rad/s] and in figure 16 d) it is 25 [rad/s]. Figures 17 a), b), c) and d) obtained from the numerical simulation have been corrected. The same forcing frequencies used in the experimental tests have been included in the simulation process.

Comments 3: Line 490ff. The original review asked whether the graph in Figure 18(b) shows the magnitude in dB for amplitude or amplitude ratio (called Ku here). It’s strongly suggested to use the latter, 20 log10 (Ku). The problem is that the driving actuator has its own frequency response, less amplitude at higher frequencies, so naturally one might expect the displacement to also decrease at higher frequencies. To effectively make the point in lines 493-494 that the system reduces vibration more effectively at some frequencies than others, you should normalize or divide by the driving amplitude.

Response 3: Thank you for your valuable comment. Figure 18b has been amended as suggested. In fact, from this graph, it is possible to estimate the points at which the gain is maximum or minimum. In this case (p = 4.0 bar), there is a local amplitude amplification for the frequency f = 2.12 Hz. For this frequency, the instantaneous effectiveness of the pneumatic vibration isolation is limited. However, in the set range (up to 6 Hz), the vibration isolation effectiveness of the system can be demonstrated.

Comments 4: Take, for example, the introductory paragraphs of the new section 3 (lines 227-257). The point of these paragraphs is to establish that machinery and vehicles have human operators, who assess conditions, execute responses, and perform actions. None of these factors are incorporated in the single degree of freedom described in section 3. It’s all rendered moot in the next paragraph (around line 261). Readers of this journal are aware that the human anatomy is complex, so all that is needed is to say “the human anthropo-dynamic model has been reduced to a concentrated mass…” Still, this is reduced from the first version, so we may proceed onwards.

Response 4: As suggested, we have dropped the description contained in lines 233-257. The information contained in these lines may be useful when presenting an anthropodynamic model such as the Wambold Model. The present work provides a basis for the analysis of models with a structure that takes into account the human internal organs.

Thanks again for your valuable comments.

Author Response File: Author Response.pdf