Friction Energy-Based Wear Simulation for Radial Shaft Sealing Ring
Round 1
Reviewer 1 Report
Contents of the paper are interested in the field of wear related to the behaviour of radial shaft sealing rings. In particular, the paper is very interesting from an industrial point of view. Based on experimentally measured total friction moments and with the help of a semi-analytical solid contact model, the modelling approach for the calculation of wear at the sealing ring is presented in the paper. The model is validated by a comparison with experimentally determined wear volumes. The semi-analytical contact model used in this publication showed itself to be particularly advantageous due to the short calculation times.
However, the manuscript still has the following problems.
(1) The authors should clearly explain the novelty of the manuscript.
(2) Lubrication is very important to wear. The authors need to explain the simplified conditions of the lubrication.
(3) References are relatively old and some new references must be introduced in the manuscript.
Final comment：
Accept after minor revision.
Author Response
Response to Reviewer 2 Comments
Point 1: The whole methodology description is very confusing and it gives the impressions that it is glued from several different parts that are incompatible. Instead of a standard contact problem solution by the finite element method (FEM), a special semi-analytical method is used, but it is not described properly. Moreover, there is still certain peas of work that should (according to authors) done by FEM to have enough inputs.
Ansswer 1.1 (on the need to integrate FEM into the semi-analytical method): Page 2 row 57-62
Here has been described more precisely the deficiency of the semi-analytical method, which should be supplemented with finite element pre-calculations.
Answer 1.2 (To the description of the semi-analytical contact model):
Here the description was divided into two sections.
The first section is in chapter 2 (page 7 row 148-184). Here the basic assumption of the half-space theory on which the semi-analytical method is based was explained and the fundamental solution of Boussinesq and Cerruti for the determination of the displacements on the half-space was explained. Furthermore, the assumption of the linear elastic behaviour of the sealing lip was explained. Due to this we are allowed to use the superposition principle in the FE model to determine influence matrices for the structural deformation.
The second section is in chapter 3 (page 7 rows 198-237). The normal displacement was used here to explain how influence coefficients can be obtained from the Boussiesq solution presented in the previous chapter. For the numerical implementation, these influence coefficients represent kernel functions and thus the determination of the displacements a convolution operation between the kernel function and the load field. The method used to solve this equation using FFT is explained in (page 8 rows 226-229).
Point 2: Similarly, there is confusing description of what is needed from the experiments to complete simulations? Friction energy density or friction work? On page 10, row 249, there is information that authors need also measured "wear volume", but I suppose that it is one of the main quantities which should be calculated?
Answer 2:
The introduction (page 3 rows 87-103) explains the significance of a wear coefficient in the wear simulation. He represents the connection between the cause of wear (friction energy or friction work) and the wear effect (wear rate). In the old wear laws such as Archard's, empirical wear coefficients are used. New approaches like Fleischer's used in this paper determine the wear coefficient from the reciprocal of the friction energy density. The friction energy density itself is an experimental parameter which is determined from the ratio between friction energy and wear volume. Thus, in order to have a meaningful wear coefficient for the simulation, friction work and wear volume are determined experimentally and the friction energy density is determined with the Fleischers approach and finally the wear coefficient is determined from the inverse value
Point 3: Very important point is the implementation of the whole procedure. Which tool and how was used for the whole methodology? There are many parts of the calculation procedure that should cooperate. Authors of this paper cite different authors mainly in the beginning of the paper and it seems that they use some fundamental parts of these cited works.
Answer 3:
The whole procedure can be considered in itself as a Matlab tool. This because the semi-analytical contact routine which represents the main part, as mentioned in row 386 (page 15), is implemented in Matlab version 2015b. This contact routine was implemented by us as for example in [2] from the publication [1] mentioned at the beginning. Especially for the contact problem between sealing lip and shaft considered in this publication, a supplement was needed to consider the influence of the structural deformation of the sealing lip on the contact. This influence was determined using one of our Finite Element Models [16] built in software Abaqus (page 9 line 253 ). The method how to determine the structural deformation matrix from the displacements determined in the FE model was taken from the publication [22,23]. A detailed description of this method would skip the frame of this publication. For this reason only the main idea of the method was explained in lines 252-273. The structural deformation from the FE model will be summarized as a matrix and used in the Matlab tool.
Point 4: suggest to present one or more flowcharts of the whole methodology in the beginning of the paper in order to make the presentation more clear
Answer 4:
Still being edited
Point 5: Mainly the overall procedure to solve conditions (6) to (12) would be very interesting.
Answer 5:
In page 15 lines 379-387, following the contact conditions, the precision was made that the semi-analytical solution of the contact problem, as described in more detail in Litteratur [1,3], begins with its formulation as a minimization problem with constraints. The contact conditions described apply as constraints. The algebraic system of equations resulting from the minimization problem is solved by the conjugated gradient method.
Point 6: The concept of total, local and structural displacements and further used rigid body motion is not consistent.
Answer 6.1 (to the concept of local and structural displacements):
The concept was introduced in this paper for two reasons. The first reason was to linearize the deformation behavior of the sealing lip, since this as mentioned in page 6 row 163 is one of the basic prerequisites for applying the half-space theory. The second reason was that due to the linearization assumption we can assume any contact displacement on the sealing lip as the sum of a local displacement (without bending the sealing lip) and a part from the bending of the sealing lip (without local deformation). In row 175 (page 7), this split was referred as the superposition principle. The local displacements can be determined directly in the semi-analytical method with the Boussinesq solution. The proportion of displacements resulting from the bending of the sealing lip is not considered in the Boussinesq solution. As described in answer 3, this fraction is determined using an FE model and added to the semi-analytical contact model.
Answer 6.1 (to the rigid-body motion):
In fact, the term rigid-body motion often refers to a concept from multi-body simulation. In order to avoid any confusion, the term has now been replaced with '' body movement ''. In the introduction on page 3 line 66-86 its presence in the semi-analytical contact modelling of fretting phenomenon was explained. For the estimation of very small tangential relative body movements that occur during fretting due to oscillating forces, there exist formulas that can be found in contact mechanical books like Johnson's book [10]. On page 13 lines 333-344 and 358-365 the presence of the body movements in the gap equations for normal and tangential contact is explained by Figure 9b.
Point 7: Is there really some advantages to use the presented approach for calculation of contact quantities instead of FEM?
Answer 7:
Yes, the semi-analytical method presented in this thesis is in contrast to the FE-Medolle in the contact determination in fact a great advantage in computing time. The first influence on the calculation time differences is the discretization in the depth direction. In the FE-approach a fine discretization of the contact surface as well as of the body depth is required to solve the contact problem. With increasing number of elements the computing time increases accordingly. In contrast to the FE method, the semi-analytical method only requires a discretization of the contact surface for contact problems. The resulting small number of elements leads to a short computing time. The second acceleration factor of the semi-analytical method is the used conjugate gradient method (CGM) (page 15 line 385) as equation solver (of the minimization problem)
Point 8: The state-of-art review in the introduction should be added as well as the novelty and originality explanation of the presented approach and explanation of paper structure.
Answer 8:
Page1 row 23-34
Point 9: The symbol of cross in the circle in eqs. (1) and (4) is probably Kronecker product and not convolution product. Could you explain it?
Answer 9:
The determination of the displacement at each discrete contact point ij with the equation (15) represents a convolution operation between the coefficient of influence to be summarized in a kernel matrix and the load field matrix. For this purpose, in the page 7 row 199-237 were provided with the help of Figure 4 detailed explanation.
Point 10: If there is not used structural deformation for measured sealing lip, what was used? (page 6, row 132)
As described in rows 298-302, the reason for this was the high calculation time associated with the FE model used for this. This lack is to be corrected however in future work.
Point 11: Gamma_c really area or rather contact line?
Answer 11:
In fact, the semi-analytical contact model presented here is a 3D contact model for this reason the size Gamma_c actually describes the contact area. The two areas in contact in the case of the sealing system are shown in Figure 7b. Due to the axial symmetry present in the sealing system, the 2D profile representation as shown in Figure 8 was used for the explanations. In order to avoid any confusion, it was agreed in rows 320-321 of page 13 that all 3D variables in the description of the contact conditions should be marked with a bracket expression (x,y).
Point 12: In figure 6, there are loads F_z, F_x on the beginning of the algorithm. What is their practical usage?
Answer 12:
At this picture, general solution process of contact with partial sliding is shown schematically. This illustration has now been described in more detail on page 12, line 333-345. For better understanding, the contact problem with partial sliding schematically shown in Figure 9 is used. Here two elastic bodies are put in contact with each other with a normal force F_z and a tangential force F_x. In the case of the sealing contact, these forces can be treated as equal to the measured radial force from Table 1 and the friction force.
Figure 10 will be made new in order to describe the entire wear simulation.
Figure 1 will be made new in order to describe the entire angle.
Author Response File: 
Author Response.docx
Reviewer 2 Report
This paper presents a method for the wear estimation in a special application of radial shaft sealing rings. The method is based on the combination of several computational approaches and a complementary experimental measurement, which is needed for certain input information. Some results of the presented method are shown in the last part of the paper and they are partly compared to pure experimental results. The topic of the paper is very interesting, however the scientific presentation is low and I suggest to rewrite the paper to be more clear and to have better scientific sound. Mainly these points should be addressed:
1) The whole methodology description is very confusing and it gives the impressions that it is glued from several different parts that are incompatible. Instead of a standard contact problem solution by the finite element method (FEM), a special semi-analytical method is used, but it is not described properly. Moreover, there is still certain peas of work that should (according to authors) done by FEM to have enough inputs.
2) Similarly, there is confusing description of what is needed from the experiments to complete simulations? Friction energy density or friction work? On page 10, row 249, there is information that authors need also measured "wear volume", but I suppose that it is one of the main quantities which should be calculated?
3) Very important point is the implementation of the whole procedure. Which tool and how was used for the whole methodology? There are many parts of the calculation procedure that should cooperate. Authors of this paper cite different authors mainly in the beginning of the paper and it seems that they use some fundamental parts of these cited works ...
4) I suggest to present one or more flowcharts of the whole methodology in the beginning of the paper in order to make the presentation more clear.
5) Mainly the overall procedure to solve conditions (6) to (12) would be very interesting.
6) The concept of total, local and structural displacements and further used rigid body motion is not consistent.
7) Is there really some advantages to use the presented approach for calculation of contact quantities instead of FEM?
8) The state-of-art review in the introduction should be added as well as the novelty and originality explanation of the presented approach and explanation of paper structure.
9) The symbol of cross in the circle in eqs. (1) and (4) is probably Kronecker product and not convolution product. Could you explain it?
10) If there is not used structural deformation for measured sealing lip, what was used? (page 6, row 132)
11) Is Gamma_c really area or rather contact line?
12) In figure 6, there are loads F_z, F_x on the beginning of the algorithm. What is their practical usage?
Author Response
Response to Reviewer 2 Comments
Point 1: The whole methodology description is very confusing and it gives the impressions that it is glued from several different parts that are incompatible. Instead of a standard contact problem solution by the finite element method (FEM), a special semi-analytical method is used, but it is not described properly. Moreover, there is still certain peas of work that should (according to authors) done by FEM to have enough inputs.
Ansswer 1.1 (on the need to integrate FEM into the semi-analytical method): Page 2 row 57-62
Here has been described more precisely the deficiency of the semi-analytical method, which should be supplemented with finite element pre-calculations.
Answer 1.2 (To the description of the semi-analytical contact model):
Here the description was divided into two sections.
The first section is in chapter 2 (page 7 row 148-184). Here the basic assumption of the half-space theory on which the semi-analytical method is based was explained and the fundamental solution of Boussinesq and Cerruti for the determination of the displacements on the half-space was explained. Furthermore, the assumption of the linear elastic behaviour of the sealing lip was explained. Due to this we are allowed to use the superposition principle in the FE model to determine influence matrices for the structural deformation.
The second section is in chapter 3 (page 7 rows 198-237). The normal displacement was used here to explain how influence coefficients can be obtained from the Boussiesq solution presented in the previous chapter. For the numerical implementation, these influence coefficients represent kernel functions and thus the determination of the displacements a convolution operation between the kernel function and the load field. The method used to solve this equation using FFT is explained in (page 8 rows 226-229).
Point 2: Similarly, there is confusing description of what is needed from the experiments to complete simulations? Friction energy density or friction work? On page 10, row 249, there is information that authors need also measured "wear volume", but I suppose that it is one of the main quantities which should be calculated?
Answer 2:
The introduction (page 3 rows 87-103) explains the significance of a wear coefficient in the wear simulation. He represents the connection between the cause of wear (friction energy or friction work) and the wear effect (wear rate). In the old wear laws such as Archard's, empirical wear coefficients are used. New approaches like Fleischer's used in this paper determine the wear coefficient from the reciprocal of the friction energy density. The friction energy density itself is an experimental parameter which is determined from the ratio between friction energy and wear volume. Thus, in order to have a meaningful wear coefficient for the simulation, friction work and wear volume are determined experimentally and the friction energy density is determined with the Fleischers approach and finally the wear coefficient is determined from the inverse value
Point 3: Very important point is the implementation of the whole procedure. Which tool and how was used for the whole methodology? There are many parts of the calculation procedure that should cooperate. Authors of this paper cite different authors mainly in the beginning of the paper and it seems that they use some fundamental parts of these cited works.
Answer 3:
The whole procedure can be considered in itself as a Matlab tool. This because the semi-analytical contact routine which represents the main part, as mentioned in row 386 (page 15), is implemented in Matlab version 2015b. This contact routine was implemented by us as for example in [2] from the publication [1] mentioned at the beginning. Especially for the contact problem between sealing lip and shaft considered in this publication, a supplement was needed to consider the influence of the structural deformation of the sealing lip on the contact. This influence was determined using one of our Finite Element Models [16] built in software Abaqus (page 9 line 253 ). The method how to determine the structural deformation matrix from the displacements determined in the FE model was taken from the publication [22,23]. A detailed description of this method would skip the frame of this publication. For this reason only the main idea of the method was explained in lines 252-273. The structural deformation from the FE model will be summarized as a matrix and used in the Matlab tool.
Point 4: suggest to present one or more flowcharts of the whole methodology in the beginning of the paper in order to make the presentation more clear
Answer 4:
Still being edited
Point 5: Mainly the overall procedure to solve conditions (6) to (12) would be very interesting.
Answer 5:
In page 15 lines 379-387, following the contact conditions, the precision was made that the semi-analytical solution of the contact problem, as described in more detail in Litteratur [1,3], begins with its formulation as a minimization problem with constraints. The contact conditions described apply as constraints. The algebraic system of equations resulting from the minimization problem is solved by the conjugated gradient method.
Point 6: The concept of total, local and structural displacements and further used rigid body motion is not consistent.
Answer 6.1 (to the concept of local and structural displacements):
The concept was introduced in this paper for two reasons. The first reason was to linearize the deformation behavior of the sealing lip, since this as mentioned in page 6 row 163 is one of the basic prerequisites for applying the half-space theory. The second reason was that due to the linearization assumption we can assume any contact displacement on the sealing lip as the sum of a local displacement (without bending the sealing lip) and a part from the bending of the sealing lip (without local deformation). In row 175 (page 7), this split was referred as the superposition principle. The local displacements can be determined directly in the semi-analytical method with the Boussinesq solution. The proportion of displacements resulting from the bending of the sealing lip is not considered in the Boussinesq solution. As described in answer 3, this fraction is determined using an FE model and added to the semi-analytical contact model.
Answer 6.1 (to the rigid-body motion):
In fact, the term rigid-body motion often refers to a concept from multi-body simulation. In order to avoid any confusion, the term has now been replaced with '' body movement ''. In the introduction on page 3 line 66-86 its presence in the semi-analytical contact modelling of fretting phenomenon was explained. For the estimation of very small tangential relative body movements that occur during fretting due to oscillating forces, there exist formulas that can be found in contact mechanical books like Johnson's book [10]. On page 13 lines 333-344 and 358-365 the presence of the body movements in the gap equations for normal and tangential contact is explained by Figure 9b.
Point 7: Is there really some advantages to use the presented approach for calculation of contact quantities instead of FEM?
Answer 7:
Yes, the semi-analytical method presented in this thesis is in contrast to the FE-Medolle in the contact determination in fact a great advantage in computing time. The first influence on the calculation time differences is the discretization in the depth direction. In the FE-approach a fine discretization of the contact surface as well as of the body depth is required to solve the contact problem. With increasing number of elements the computing time increases accordingly. In contrast to the FE method, the semi-analytical method only requires a discretization of the contact surface for contact problems. The resulting small number of elements leads to a short computing time. The second acceleration factor of the semi-analytical method is the used conjugate gradient method (CGM) (page 15 line 385) as equation solver (of the minimization problem)
Point 8: The state-of-art review in the introduction should be added as well as the novelty and originality explanation of the presented approach and explanation of paper structure.
Answer 8:
Page1 row 23-34
Point 9: The symbol of cross in the circle in eqs. (1) and (4) is probably Kronecker product and not convolution product. Could you explain it?
Answer 9:
The determination of the displacement at each discrete contact point ij with the equation (15) represents a convolution operation between the coefficient of influence to be summarized in a kernel matrix and the load field matrix. For this purpose, in the page 7 row 199-237 were provided with the help of Figure 4 detailed explanation.
Point 10: If there is not used structural deformation for measured sealing lip, what was used? (page 6, row 132)
As described in rows 298-302, the reason for this was the high calculation time associated with the FE model used for this. This lack is to be corrected however in future work.
Point 11: Gamma_c really area or rather contact line?
Answer 11:
In fact, the semi-analytical contact model presented here is a 3D contact model for this reason the size Gamma_c actually describes the contact area. The two areas in contact in the case of the sealing system are shown in Figure 7b. Due to the axial symmetry present in the sealing system, the 2D profile representation as shown in Figure 8 was used for the explanations. In order to avoid any confusion, it was agreed in rows 320-321 of page 13 that all 3D variables in the description of the contact conditions should be marked with a bracket expression (x,y).
Point 12: In figure 6, there are loads F_z, F_x on the beginning of the algorithm. What is their practical usage?
Answer 12:
At this picture, general solution process of contact with partial sliding is shown schematically. This illustration has now been described in more detail on page 12, line 333-345. For better understanding, the contact problem with partial sliding schematically shown in Figure 9 is used. Here two elastic bodies are put in contact with each other with a normal force F_z and a tangential force F_x. In the case of the sealing contact, these forces can be treated as equal to the measured radial force from Table 1 and the friction force.
Figure 10 will be made new in order to describe the entire wear simulation.
Figure 1 will be made new in order to describe the entire angle.
Author Response File: Author Response.docx
Round 2
Reviewer 2 Report
The authors improved the paper and answered all questions. Thus I reccomend to consider this manuscript for publication.
