Optimal Magnetic Spring for Compliant Actuation—Validated Torque Density Benchmark†
Round 1
Reviewer 1 Report
Focusing on Elastic actuation, we are attempting optimization design by various approaches. Several basic structures have been proposed and used for analysis. In addition, detailed analysis was done along several evaluation items, and it was able to be read very clearly. It is highly appreciated that the prototype of the actual machine for analysis is verified. The proposal and the question are shown below.
1. Evaluation items have costs, but how are they calculated? Calculation is possible if it is only material cost. However, the production costs are considered to involve various items. For example, personnel expenses, processing costs, number of productions, etc. can be mentioned. How did you calculate it?
2. I believe that the persuasive power of the paper will increase if there are more than one actually produced. Even if there are not multiple prototypes, I think there are several methods. For example, I think that describing what can be considered in the error between the analysis result and the actual machine will clarify the analysis result more.
Author Response
1. Evaluation items have costs, but how are they calculated? Calculation is possible if it is only material cost. However, the production costs are considered to involve various items. For example, personnel expenses, processing costs, number of productions, etc. can be mentioned. How did you calculate it?
--> This is a valuable comment, as we didn't previously indicate explicitly that we use the bulk cost. Also the meaning of using only bulk costs, makes it possible to compare between different magnetic spring designs, under the assumption that magnet manufacturing is not significantly different between different magnet geometries. We have added a paragraph to explain the cost definition within this paper. Also, the limited utility of this cost formulation is explained
2. I believe that the persuasive power of the paper will increase if there are more than one actually produced. Even if there are not multiple prototypes, I think there are several methods. For example, I think that describing what can be considered in the error between the analysis result and the actual machine will clarify the analysis result more.
--> This comment goes into methodology, and we agree with it. However, for the time being we can only produce virtual data (CAD + FE model) of some other geometries as an additional virtual validation of the 1D model. Seeing that the other reviewers had a similar comment we have spent most of the effort in updating the paper, generating these points and collecting the previously generated points design points (visible in the updated figure 12). Additionaly we've spend some effort to explain figure 12 in greater detail.
Reviewer 2 Report
In the paper, the authors discuss the benefits of using magnetic springs in elastic actuators, giving examples for series elastic actuators. An experiment is made to help validate their design methodology as well as some modeling work. This is a beneficial study to undertake, but the different sections don't feel connected and the overall structure is very hard to follow.
Overall, there is some really useful material here. However, the presentation is very choppy, leading the reader to need to try to interpret the authors' intent/meaning/direction. I've put in some comments below, but essentially I would recommend a very thorough editing/rewriting of most of the material here.
-There seems to be a back and forth in the usage of the terms "service robotics" and "industrial robotics", please harmonize usage or define both.
-The introduction begins in robotics and then pivots (paragraph beginning line 57) to machinery in general (drivetrains, vibration isolation, etc).
-While I think this is a highly worthwhile study, it should be pointed out in what conditions magnetic springs should not be used (are there electric/magnetic field constraints? temperature? shock loading?) The authors discuss temperature in depth, but commenting on the other fields would be useful. Essentially, why aren't magnetic springs more widely adopted?
-Could a comparable chart be made as that in Ashby (1999) that gives a design chart for strength/weight ratios etc for different magnet materials?
-Line 102, is torque density really equivalent to actuator bandwidth?
-Figure 3 and in general, please define variables (in this case, B and H), no matter how basic - wide readership in Actuators. This comment applies very much throughout the paper (for example, not everyone knows what a PMSM motor is).
-Paragraph starting in line 112, please clean up. What is 30.79%? What is SmCo? There's just a lot of information here that isn't defined/introduced really.
-In Section 2, please state early on that you are implementing a rotary spring arrangement for all your experiment/modeling/discussion (even though it applies to both rotary and linear springs).
-Figure 6 vs Figure 7: it looks like in the experimental setup you have several anti-backlash couplings (you mention them in the paragraph above Figure 7) in your experimental rig - these would essentially be traditional series elastic actuators with a magnetic bearing in the middle, correct? I'd like to see commentary on that effect.
-Table 2: What rotation is the high accuracy optical encoder measuring?
-What are all the variables in equation 3?
-Figure 8b: what was the forcing that resulted in this torque? Why does the bearing model+ CAD offer such a poor dynamic prediction? What is the static loss hypothesis? What is the validation model?
-Table 3: Coulomb friction should not have units, correct? In the equation 4, is T_c coulombic friction or torque from friction? This may be a case of different fields referring to Coulomb friction as very different things - I would be careful to differentiate it from the Coulomb friction model (mu times normal force) if you mean something else.
-Figure 9: I believe the three plots are the phases referred to above? Please spend more time discussing these phases.
-Figure 9 phase 0 startup: you mention the difference in energy needs between the two, but the spring assisted design also requires the motor to switch directions of torque application ~13 times while the no spring assist requires ~3. Please comment on motor lifecycle concerns. Similar question with the middle part of Figure 9 - the first transient sees fewer direction changes with no spring, later transients see more direction changes with no springs.
-Figure 9 phase 3 referred to at line 271-272 - the plotted energy is reset in the middle of the experiment? What do you mean, here? Do you mean the torque level is reset to zero for the spring assisted? It sounds like you're saying the first ms of the third phase would be a one time thing, and then the three pulses afterward would be an ongoing torque buildup?
-Figure 12: Where is the equation for this 1d model? how much variance is there between the model and a fit to the data you have plotted here? I would suggest not including this or adding some points at other energies, otherwise it looks very sparse and unconvincing.
-Figure 13: please explain the comment that magnetic springs have increasingly higher energy density for high life cycle numbers from 10e7 and beyond? Nothing appears to be crossing on your plot at that point. This section of the paper could use commentary on how common lifecycles in the gigacycle range are needed.
-Figure 14: what are the solid lines? Magnetic spring models? Are these your 1D models or more complex models? If 1D model, please show the range of the model that is predicted from figure 12 (which shows there should be significant uncertainty it appears).
-In conclusions, I think this would be a good point (or somewhere else) to discuss what price discrepancy is between mechanical and magnetic spring - reducing down time of some lines would probably make it worthwhile to convert to magnetic springs. However, in systems whose down times are dictated by other parts or less expensive production lines, magnets must be more expensive than the highly commoditized spring.
Author Response
In order to address completely the extensive comments of the reviewer 2 we have split them into:
- methodological
- technical (typos, inconsistencies, clarity etc.)
METHODOLOGICAL (also pointed out by the other reviewers)
-Figure 12: Where is the equation for this 1d model? how much variance is there between the model and a fit to the data you have plotted here? I would suggest not including this or adding some points at other energies, otherwise it looks very sparse and unconvincing.
--> We have added 2 additional points in figure 12 based on virtual designs. It is normal and expected, that there is an "error" between 1D model and multiple designs with the same specification, as in a pareto-front in figure 7 we have a trade-off between cost and inertia. What we are trying to capture with the 1D scaling models is the knee-point of the pareto curve in figure 7 for different energy requirements/ spring sizes. We disagree with use of variance to characterize the skewed distribution due to a prominent knee in pareto front/ large hypervolume under the pareto curve. Alternatively, we could possibly plot box plots of virtual validation data for each energy value instead of plotting each validation design as a point.
TECHNICAL (improving text clarity, figures, typos etc.)
-There seems to be a back and forth in the usage of the terms "service robotics" and "industrial robotics", please harmonize usage or define both.
-The introduction begins in robotics and then pivots (paragraph beginning line 57) to machinery in general (drivetrains, vibration isolation, etc).
--> It was never the intention of the authors to use these two terms interchangeably. Instead of providing a reader with the definitions, we reserve the use of service robotics to the cited publications which are addressing only quasi-static applications with low lifetime requirements. We do, however, advise extending the use of elastic actuation concepts to industrial robotics and wider family of highly dynamic industrial actuators, with help of magnetic springs. We cannot report on usage of elastic actuators in neither industrial robotics or other highly dynamic industrial actuators. To sort out the confusion we have explicitly stated this intent in the first paragraph of the text.
-While I think this is a highly worthwhile study, it should be pointed out in what conditions magnetic springs should not be used (are there electric/magnetic field constraints? temperature? shock loading?) The authors discuss temperature in depth, but commenting on the other fields would be useful. Essentially, why aren't magnetic springs more widely adopted?
--> We consider that due to the limitations of permanent magnet materials, environments where PMSM can operate is considered to be suitable for magnetic springs. We considered this somewhat obvious, but in light of the reviewer comments we have added a brief section with this explicit statement.
-Could a comparable chart be made as that in Ashby (1999) that gives a design chart for strength/weight ratios etc for different magnet materials?
--> The provided strength/ weight ratio in table 1. answers exactly the question of strength weight ratio. In fact it gives an energy density and an adivsable operational temperature for different magnet materials, so it provides more information than the reviewer asks for. Following a reviewers comment on SmCo, we also added another specific material to the table.
-Line 102, is torque density really equivalent to actuator bandwidth?
--> The expression in question has been removed and replaced with a more suitable expression.
-Figure 3 and in general, please define variables (in this case, B and H), no matter how basic - wide readership in Actuators. This comment applies very much throughout the paper (for example, not everyone knows what a PMSM motor is).
--> PMSM had already been introduced in original version as an acronym in line 84 (see 1st draft), as advised in Actuators - Instruction for Authors ; B and H have been introduced, following this comment.
-Paragraph starting in line 112, please clean up. What is 30.79%?
--> This is indeed a well spotted typo in the 1st draft text. Following the reviewers comment, It has been corrected.
What is SmCo? There's just a lot of information here that isn't defined/introduced really.
--> Replaced with a full name with properties introduced in table 1. See comment on table 1 above.
-In Section 2, please state early on that you are implementing a rotary spring arrangement for all your experiment/modeling/discussion (even though it applies to both rotary and linear springs).
--> This is indeed a relevant comment, and although the 1st version has this mentioned in abstract, we recognize that it should also be explicitly stated in the body of the text.
-Figure 6 vs Figure 7: it looks like in the experimental setup you have several anti-backlash couplings (you mention them in the paragraph above Figure 7) in your experimental rig - these would essentially be traditional series elastic actuators with a magnetic bearing in the middle, correct? I'd like to see commentary on that effect.
--> We disagree with the comment of the reviewers about bellow couplings making the system under study an SEA. In fact, there are several elastic components in this system ( e.g. torsional shaft deformation, torque sensor deformation) that doesn't neccesarily make it an SEA. Bellow couplings here are selected purely to avoiding misalignment issues in a modular setup. Otherwise, these are significantly stiffer than the parallel magnetic spring. Anyway, a sentence addressing the series elasticity of the couplings has been added. It is author's opinion that further details about the couplings will burden the manuscript without adding value.
-Table 2: What rotation is the high accuracy optical encoder measuring?
position on spring and flywheel as indicated in the table. In table, it has been added that there are two sensors, to avoid confusion.
-What are all the variables in equation 3?
--> A brief explanation of each parameter has been introduced.
-Figure 8b: what was the forcing that resulted in this torque? Why does the bearing model+ CAD offer such a poor dynamic prediction? What is the static loss hypothesis? What is the validation model?
The bearing model is based on a priori data. It's in fact an initial guess at the friction in the system.
-Table 3: Coulomb friction should not have units, correct? In the equation 4, is T_c coulombic friction or torque from friction? This may be a case of different fields referring to Coulomb friction as very different things - I would be careful to differentiate it from the Coulomb friction model (mu times normal force) if you mean something else.
In motion modeling and control, friction is commonly defined as force and is measured either in newtons for linear motions systems or when applied over a lever as Nm in rotational systems. Force in the coulomb friction model is the in newtons while friction coefficient mu is a dimensionless scalar. Coulomb friction is a term commonly used as an speed independent force. By extensions to rotational systems Coulomb friction torque is used in units of Nm here. The use is the same as here: https://nl.mathworks.com/help/physmod/simscape/ref/rotationalfriction.html
We have additionally changed the table entry to Coulomb friction torque to avoid confusion.
-Figure 9: I believe the three plots are the phases referred to above? Please spend more time discussing these phases.
-Figure 9 phase 0 startup: you mention the difference in energy needs between the two, but the spring assisted design also requires the motor to switch directions of torque application ~13 times while the no spring assist requires ~3. Please comment on motor lifecycle concerns. Similar question with the middle part of Figure 9 - the first transient sees fewer direction changes with no spring, later transients see more direction changes with no springs.
-Figure 9 phase 3 referred to at line 271-272 - the plotted energy is reset in the middle of the experiment? What do you mean, here? Do you mean the torque level is reset to zero for the spring assisted? It sounds like you're saying the first ms of the third phase would be a one time thing, and then the three pulses afterward would be an ongoing torque buildup?
--> We understand that the mislabeling of the y axes has cause an issue with the image understanding. Please refer to the corrected version, as we believe it makes the graph clearer now.
-Figure 13: please explain the comment that magnetic springs have increasingly higher energy density for high life cycle numbers from 10e7 and beyond? Nothing appears to be crossing on your plot at that point. This section of the paper could use commentary on how common lifecycles in the gigacycle range are needed.
--> this is indeed a very relevant comment regarding the lifetime requirements. The number 10e7 and beyond was rather a rule of thumb than a real cross-section in this plot. We did however, spot in some of the points in this section of the plot (both for 1e6 and 1e9 ) that the realistic mechanical spring designs become significantly lower in energy density than the designed magnetic springs. The issue with spring failure is a stochastic problems. Second, depending on the operational frequency of the system . However, here we are trying to purely address the design of magnetic springs without extending the work too far in the system considerations regarding use of magnetic springs in highly dynamic drivetrains.
-Figure 14: what are the solid lines? Magnetic spring models? Are these your 1D models or more complex models? If 1D model, please show the range of the model that is predicted from figure 12 (which shows there should be significant uncertainty it appears).
--> The figure shows 1D model(lines), we have ensured that the validated model range from figure 13 corresponds to models shown in figure 14.
-In conclusions, I think this would be a good point (or somewhere else) to discuss what price discrepancy is between mechanical and magnetic spring - reducing down time of some lines would probably make it worthwhile to convert to magnetic springs. However, in systems whose down times are dictated by other parts or less expensive production lines, magnets must be more expensive than the highly commoditized spring
--> we can only make a very general statement about bulk material cost. However, the magnetic springs we introduce can take over a function of multiple mechanical components, namely mechanical springs and cams, or mechanical springs and other mehanisms. In general operational frequency of the system is a good indicator for magnetic spring need.
