วีดีโอ

I'm happy that these lectures actually help!

Glad to help!

I have a video that explains how to create the spreadsheet, I do not provide them. Also, I do not have a lecture on cylindrical vessel welds...but the same ideas would be used. The interesting part is the transition form hoop and axial stress as you move to the end cap...this causes interesting stress concentrations!

You are correct....I just defaulted to kc=1 for the sake of simplicity! and many students get rather overwhelmed by the marin factor adjustments, though this factor is the easiest to understand.

Thank you! I visited your channel and saw a number of wonderful machines!!

Thanks! Glad it resonated.

This is from the Shigley textbook.

It is a compressive normal stress, so the sign is negative.

If the mean stress is zero you are intersecting the stress amplitude axis where all lines converge...so the factor of safety is just equal to the stress amplitude divided by the endurance strength. Thank you for asking this question, because the Gerber formula does not work when the mean is zero!!

I am terribly sorry...I did not include the correction factor table, Table 4.1 in the Shigley text. You may recall that for simple bending, the shear stress is parabolic, with a maximum at the neutral axis. To get a precise solution, you need to integrate that functional form across the beam height and beam length. This correction factor provides a simple approximation that side steps that process.

The chart I show is just a portion of the bearing catalog. You would need to go to a comprehensive catalogue from the supplier you want to use. For instance, you could go to the SKF online catalogue and enter the dimensions of your shaft and it directs you to a bearing. The lecture here, is showing you a procedure that you can use to double check what the suppliers suggest when they point you to an online calculator. You could also go to the online pdf catalogue for Timken, or NSK, or Fersa or Schaeffler. There are many sites you can choose from. Pick the supplier that offers the best combination of price and reliability that can deliver to your location.

What a surprise!! I had the same problem

There is a tutorial video that explains what to do. I don't share the files because I often assign this task to my students!!

You have 2 main options: 1: Just build the shaft and run an FEA analysis in the manner I showed; or (2): Use a lumped mass model in the basic equation. You can choose the smallest diameter section and treat that as a uniform shaft the entire span...then add lumped masses to that uniform shaft that are associated with the changes in diameter and combine the uniform shaft and the lumped masses using Dunkerly's equation. The more 'lumps' you use, the better the approximation. Remember to not include the uniform shaft in the 'lumped' masses. Imagine those shoulders as extra weight added to the uniform shaft. Does this make sense to you? Regardless, I would compare a hand calc to an FEA to make certain you are getting similar answers.

I want to caution you on using the approach I recommended above...it will give you answers that are well below the reality. If you do what I suggested, you are going to add mass to the smallest 'effective ' diameter shaft...this will be much more compliant than the true shaft, and will give a whirling frequency much lower than the true answer. I am currently writing code in Excel to partition the shaft into segments but account for the changing diameters as part of that partition. It is pretty tricky code, but I will press on with it. I am doing it in Excel, not because I like VBA, but because nearly everyone has it. Your best option is to use FEA code to analyze the whirling.

No...it is not naturally leak resistant. You can, however, purchase a sealed bearing that will incorporate a polymer seal that also slides against the shaft. They increase friction and will, eventually wear out. Water resistant is also a lot different from water proof. If all you need is water resistance, then you could probably use a sealed bearing. Your best bet is to go to the SKF or Timken or other manufacturers site and open a chat to discuss options. There are seals, alone, that are designed to isolate locations on the shaft...but these are different from bearings...think of a crankshaft seal on a car, for instance, or seals that are required for prop shafts in boats/submarines. Sealing against pressure is a tough proposition that gets expensive.

Pramath...good question. I want to constrain translation, but allow rotation. that is why I chose this approach. So I fixed the x,y,z coordinates of one end, and just the in-plane coordinates at the other. But there is a better way...if you put a small hemispherical impression at each end, then use a frictionless constrain, it fixes the location of the shaft ends, but allows for rotation. It is always a challenge to find appropriate constraints, I must say. So, whatever you choose to do, do not analyze the results near those constraints...also, just change the constraints and observe how it changes the results. This is an eye opening experience for all of us, students especially. In fact, I love that FEA allows one to run a host of 'experiments' that help you develop understanding.

@@MechaTomics I'm getting the bearing loads very high near the split faces, and I think it's because the area is very small, causing it to fail unreasonably. Should I increase the width of split face or is it a different problem causing. Also, I very much appreciate your last reply, learning a lot from your videos. Thank you! :))

@@pramathbhat6423 You will definitely have extremely large bearings loads at the split faces...you can not trust those numbers, because they are a poor representation of how the loads are actually applied. As usual, you need to keep you analysis away from the points where you apply constraints. It does not mean that you can not do it differently to get what the actual distribution of the bearing loads happens to be, but you can not get it from what I proposed doing here. You would need to actually sort out the contact area for a real bearing...it can be done, but that is not what I was trying to do here. Bottom line is that you've got the correct intution...your bearing loads are high because of the artificial area you are choosing to support those loads! So, I would say, good job! It is very important to look at your results and check them for reasonableness. You found them to be unreasonable, so you know that the answer is incorrect. I repeat: good work!

Thank you for the kind comment. I have plans to do more, but always run into time constraints! If it helps in any way, I am happy.

@@MechaTomics I appreciate your efforts. I understand it's not easy to manage time especially with such complex topics. I am rather impressed on how you could present these concepts clearly and concisely.

@@MechaTomics I want to propose, if you don't mind, that you maximize the writing ✍️ and minimize PowerPoint. I know many people understand more as they observe the teacher writing down stuff instead of just showing a typed page because that's what we are going to do in tests and practice. Also, please could you make videos to show how you develop your excel sheets? I found them so helpful and easy to do design with them. I know these will not be easy to implement, but I would really appreciate.

@@Mr_mechEngineer I do agree with you . As I move into retirement I am going to redo all of these topics and attempt to make it better.

@@MechaTomics thanks so much. My engineering education will benefit highly.

Shigley's Mechanical Engineering Design text has the images, otherwise I imported CAD drawings into Fusion 360 using the import part menu item. I import the CAD drawings from McMaster Carr,

Return period is the inverse of the annual probability. So you would need to know the annual probability of a storm of any given size in a single year. As to wind speeds...you got me there. I would really have to think about this. It could well be a 3 parameter weibull with 0 as the minimum wind speed, then a shape parameter that makes it look like a power law. But I really don't know and would have to do some research on that! Good question!

@@MechaTomics Thank you very much for the response. It helps.

You are quite right! They are rarely, if ever, a single diameter. I will do it.

@@MechaTomics Thank you so much!

You are most welcome. Good luck with your studies!

Darshan. I do not use ANSYS, so I am not qualified to comment. However, any FEA program would work well. I now use COMSOL for most of my FEA, and just use Fusion 360 for a first look. This is a solid mechanics problem, so it is a pretty good problem for any FEA package. I thought Fluent was a fluid program (CFD)? IF so, you do not need it for this sort of problem.

You needn't make a correction if you do not have an axial load.

Yet more info for you. You start with a guess. I always start with Fe=Fr. Then you select a C10. get the C0, and find an updated e by computing Fa/C0. You then select the X and Y values and update your bearing selection....you keep iterating until you get no change in the selected C10 value.

It would be totally sensible to do as you say if fatigue was not so emperical. But there are threshold loads below which your part will last indefinitely. So, the approach presented here is a 'design' approach to determine an equivalent radial load that would have the same lifetime. It comes about from a large number of experiments, not a first principles calculation. That said, you could do a thorough analysis and determine the contact loads in the bearings, then determine the endurance strength and compare the loads. The approach presented is just a simple, time-tested, approach to make it easier to design the bearing. It incorporates a fairly significant factor of safety, as do nearly all of our simplified design calculations. I encourage you to keep thinking as you do, question everything, and determine which topical areas you would like to pursue. It may be that you advance the field in a meaningful way.

I also forgot to mention that the selection tables are based entirely upon radial loads applied to the bearings. So, to use the bearing selection tables when you have a combined axial and radial load, you need to find an equivalent radial load. Think of this in the same way you use the von Mises criterion to find an equivalent uniaxial load from a multi-axial loading state. But in this case, you are using equations that are based upon experiments and curve fitting, not some meaningful mechanics calculation.

This does seem a bit odd, I admit. But you need to select a dramatically over-rated bearing if you want a high lifetime with a high reliability. The tabulated values are only good for a 50% reliability. So, if I want, for instance, a 98% reliability of the bearing for the given lifetime, I need to select a much 'stronger' bearing. If you watch the lecture on bearing reliability shifting, it will begin to make sense. I hope!

Aidan: If you look at the hoop stress equation the only negative value is the last term, so the answer can only become negative if that last term dominates. I am guessing that there is a numerical error in how that last term is calculated. That pre-factor that contains the Poisson ratio. If you do this in excel you have to be very careful about placing parentheses around the correct terms so the order of operations is what you want it to be. You need to calculate like this: ((1+3*nu)/(3+nu))*r. If you aren't very careful you end up with operator orders that change the answer. The other problem is that you need to fix the cell number where you have Poisson's ratio, or just numerically enter Poisson's ratio into the equation...because excel tries to move down the column for every element in an equation.