Welcome to The Mentored Engineer. In this video, I’m going to show you a way that you can make me cringe. Okay, so we’re going to talk about gussets, and gussets are one of those areas where I’m just like, ooh, this is so simple. Why do people keep doing it wrong? And it makes me sick.
All right, so let us look at a cantilever beam system right here. Let’s say it’s like a street light or something. And we have a square tube butting up with another square tube. Now, as you can imagine, I will load it here. It’s going to be a cantilever beam and then a constant moment cantilever beam all the way down to the ground.
All right. Right here at this joint is where it obviously causes us problems. Now, the cause right here is stress flow and it’s everywhere. I mean, we’re just stresses need to change direction. And when you change it 90 degrees, that’s it’s hard to do without extra pieces of steel and extra design time.
OK, so I’m going to show you how a couple different ways to make this joint better and one that I really hope that you don’t do because it makes me cringe okay so if I look closer at this area right here here’s what I’m I would want to see all right I’m going to have this tube here and it’s going to have its wall I want to have it transition to this one. The first thing I’m going to want to do is I’m actually going to want to set this tube just a little bit higher so that I can get good stress flow.
The top of this vertical tube is going to be right here, and I’m going to have my dotted lines. When I think about stress flowing, it’s flowing in the top of this beam very nicely. It’s all uniform. It’s all going. You’ve seen this on an FEA plot where, man, it’s just going smooth.
All of a sudden it comes to this tube and there’s nowhere for it to flow. We’re going to change that. The first thing we want to do is we want to cap the end of this plate. And we’re going to use that with the same thickness as this tube, if not thicker. And then we’re going to come back and fill this spot up with weld.
And now I have a nice path for my stress to flow. through this joint all the way back here to this back wall and as it goes through this plate it’s actually going to distribute to the sides of this beam very nicely and you’re going to have a great transition so do that another thing you can do is actually have this plate come over and cap this one but then you have to worry about different stress transitions with transverse welding and stuff like that so that actually may have more complications than it’s worth so I would do this All right, so if I have the room, I can get down in here and weld this, weld another plate down there.
I want to do that. All right, and there’s a very specific way you want to do that. You actually don’t want to line it up with the material at all. It’s kind of weird. All right, so I’m going to put in a fillet weld right here.
All right, and I want to actually have my plate come down to the toe of this fillet weld. right there now you think that’s kind of weird but it actually makes the stress flow great so I’m going to put a fillet weld right here because that’s likely the only place I can get in with a welding torch is coming down right there and keep in mind this actually has to be quite a big tube to do this all right
and I can see that my stress flow will flow through here come down here into that weld and into that plate and it makes a nice smooth line and that’s what we’re looking for stress flow is like water if the if there’s enough material and the stress flows your water is nice and calm and clear on the top as it gets shallower and moves quicker, I’m going to see a lot more hot spots and a lot more motion in water. So that’s why we say stress flow flows like a river. All right, so nice, even stress flow through that material.
Okay, now if you can’t do that, you’re going to have to look to gussets. So, let’s redraw this and look at some gussets here. all right now the first thing and this is what’s going to make me cringe is I come in here and see a gusset of that nature may not be exactly that profile but if I look at the end here I see a tube and I see another tube and that gusset centered right in the middle of the tube don’t do that it makes me very upset okay very upset all right there’s no reason to do this
all right so first of all you have you have nothing behind this gusset on this plate to take load it’s just going to bend that plate it’s already your highest stress surface right there why would you add another plane of stress there so don’t do that okay it’s just dumb you’re going to push up you’re going to bend that thing and it’s already bending in another direction Don’t do it.
Stop it. All right, so the next solution, and I like this one somewhat better. If I go in here and actually modify this a little bit, my tube actually has a radius corner. All right, so what I can do is go in here and add a gusset, and I can weld right back in here where that J-bevel would be and do the same thing over here. And I at least have something on both surfaces where I’m pushing directly into a wall behind it.
Much better. Good job. Give yourself a round of applause for thinking of that all by yourself. Okay. And that’s good.
It’s better. It’s not the best. Alright, the problem with this is that you still have your highest stress right on that tube, on that outer surface. And you’ve added a lot more area moment of inertia with that gusset. And drastically.
And that’s going to put a hot spot right here. Especially right there. It’ll be a lesser one right there. And that’s… No matter what you do, you’re still going to have that.
If you drag this down, you’re still going to have it. In fact, almost anything you do is still going to have it, but we can minimize that as much as possible. And the way we do that is by placing the gusset outside of the beam, or outside of the tube, not on the edge of the tube. All right, so we’re going to want to start with our gusset and it’s going to go on the side, each side of the tube on the outside. And it’ll go right down here because this is what, it’s the neutral axis.
And when we pick that up, we’re going to have a stress concentration at the end of that. But if it’s on the neutral axis, who cares? All right, so we’re going to bring this down and it’s going to go this way. down this beam a lot farther than it will down this way. Alright, and we’ll round that up.
We’re going to bring it down to the edge of the tube, and we probably want to do so at a 30 degree angle or so. It doesn’t need to be very wide, you know, 15 to 30 degrees is probably where you want to be. And right as you get here, to this edge, you’re going to want to make it flat for just a little bit. You’re going to make a nice smooth transition. You’re transitioning grate into the radius area.
You’re going to have a little bit of a lateral weld there. And you’re going to be increasing your section modulus without a dramatic increase in your area moment of inertia. I could go into a whole video on that as well. So, I won’t bore you with that here, but that’ll probably come out pretty soon. Now what we’re going to do is we’re going to start going back on our 30 degree angle here.
And then we’re going to make our transition here and we’re going to radius that back up. and go to our point now this one doesn’t need to be as as critical as this one this one is trying to get that in there this this whole tube it just acts differently I can’t explain it very well but when you look at it in FEA it’s just not a problem so a lot more forgiving on this side of the equation than on that side all right so that is how you make a great gusset all right don’t make me cringe I don’t want to have to find your design know
that oh my gosh you watch this video and you still did that so I implore you to make your gussets as much like this as you can and do it every time a lot of times this will save you even having to do any FEA on it just because it’s such a great design all right well thank you for watching this episode.
7 Tips for Designing Excellent Tube in Tube Sliding Joints
Sliding joint mechanisms are everywhere. We see them on mobile equipment outriggers, sliding glass doors and scissor lifts. I made a critical mistake on my first tube in tube sliding joint. I’ll share the details of that with you so you don’t make the same mistake or any other.
When designing a sliding joint, you will need to:
Decide to use Wear Pads or Rollers
Watch the Contact Stress
Decide if the Joint Needs to be Powered
Plan for Load Reversal
Plan for Noise
Plan for Slop
Plan for Assembly and Maintenance
Tube in Tube Joint Overview
Typical ‘Out and Down’ outrigger assembly
Tube in tube joints are one of the most common design structures. Whether round, square or rectangular these joints are everywhere. You don’t even have to use structural shapes for these designs and can make your own custom shapes.
Generally speaking you will want to have about a 3:1 overlap on the inside members height dimensionwhen extended. This means that if I have a 5″ x 4″ tube, I would want the minimum overlap at full extension to be 15″ (5″ x 3). This will minimize play in the joint and minimize the contact forces on the tube walls.
You will also want to make sure that the overlap at full extension is at least 25% of the total stroke. This will maintain a fair level of stability in the joint.
The extended overlap has just less than a 3:1 ration for the tube height of 6.00″. The target should be 18.00″ The change in overlap from stowed to extended is 17.00″ / 41.50″ or 41%.
If the design isn’t loaded when sliding, you can get away with eliminating wear pads and/or rollers. A music stand’s height adjustment is a good example of this. Round tubes are generally the best choice for these types of situations because the OD and ID of the tube are controlled. You can select tubing sizes to minimized play in the joint
This light stand is a metal on metal round tube assembly. This is a good design choice because it is lightly loaded and doesn’t move under load.
However, if the apparatus is loaded when it moves, this design will wear out very quickly, especially if it is metal on metal.
The main down side of using round tubing is you can’t prevent rotation naturally. You will need another mechanism to do that. This is where rectangular tubing comes in handy.
Square or Rectangular Tubes
Square and rectangular tube in tube designs will naturally prevent rotation of the inner component. Additionally, they give you a great surface to mount slide pads or run cam followers.
The major down side is the end of the tube will need to be reinforced. As the tube is loaded, the loads will tend to yield the end and cause it to look like the horn of a tuba. Not good! However, this is a proven design and it will work.
FEA results for typical tube in tube design. With linear analysis, the top tube wall will act as a beam. Non-linear analysis will have the corners of the tube yield and the top wall will start acting as a tension only member.
It works because once the material has yielded, it will redistribute the stress. In the initial loading, the material will bend. Since it is thin, there isn’t much resistance to bending so it yields and makes the horn shape. As the loading continues, the material starts to transform and the bending load converts to a tensile load and acts like a rope with constant stress throughout the material.
Reinforcement
While this, structurally speaking, will probably work for most designs. No one wants to walk up to a machine and see a horn shaped tube! It also makes the joint have a lot of extra play that can’t be changed. The solution is to reinforce the end of the tube.
The first step to reinforcement is hand calculate the stress on the tube as if it is a simply supported beam with a load in the center. I choose simply supported because we do not want the sides of the beam intentionally carrying moment. The length of the beam should also be the maximum width of the tube.
I also suggest using a point load at the center not only because it will be easy to calculate but also it is the worst case. With slide pads, we can’t be assured that the pads will contact in the way we want. If there is a torsional load, we will be contacting differently than in pure bending. (More to come on that)
You may also want to reinforce the sides to deal with the extra load and amplify the stiffness. While we assumed a simply supported load, it doesn’t mean that it is simply supported. Those corners are still taking some moment.
The same design with reinforcement plates dramatically lowers the stresses.
Strengthening the Inner Tube
The contact forces between the tubes can be quite large. In the previous section, we discussed how to stiffen the end of the outer tube. Well, we are half way there. We now need to address the inner tube.
While we can add material around the outer tube of our sliding system, it is often more challenging to add material to the inside of of the inner tube. Quite often there is a cylinder in the way that makes structural improvements very difficult.
Another complication is if the outrigger moves under load or can extend to various positions. If either of these situations are in your design, you will probably need to add doubler plates under the wear pads for strength. To decrease the moment on the inner tube, you can split the wear pad and have the only the corners contact.
FEA results with reinforced inner tube with web plates.
If your design is unloaded when it is sliding and always extended to the same place(s), you can add web stiffeners to the inside of the inner tube. The web plate is the best way to transfer the contact load to the side walls. An oval or slot shaped hole can be added to the center to allow a cylinder and any hoses or wires that need to travel with the sliding section.
1. Should I Use Wear Pads or Rollers?
Using wear pads or rollers is always a tough decision. This guideline should help you to make that decision.
As a rule, I always start my design with the intent of using wear pads. As the design progresses, I will keep in mind the following conditions and switch to some sort of roller system as needed.
Heat Generation
Wear pads are friction members. If extending under load, they produce heat! Since they are plastic, they can melt pretty easily. They need time to cool off in between cycles. I would suggest less than a 25% duty cycle on wear pads. Switch to roller bearings if the duty cycle is too high.
Also, the maximum speed of the tube is critical. Depending on your material speeds of up to 10 fpm to 25 fpm are acceptable. Experimentation in your application will be necessary.
OSHA Requirements
If this is an unpowered sliding system (meaning it is powered by a human being), OSHA has a lifting limit of 50 lb. While I am not sure if this translates directly to pushing or pulling items, I still think that it is a good limit to design for.
In design, I would plan on using only 60% of the 50 lb or 30 lb as the maximum limit that the operator will exert. Be sure to calculate the additional forces if this is used on a slope. This way when the unit is fabricated, you have some tolerance in the design in case the the tubes are tight and it requires more force than expected to extend.
To reach this goal, you may have to change from sliding wear pads to rollers. This move will add some cost and complexity, but it can drastically reduce the force required to slide.
2. When to use Powered Extension
As mentioned in the previous section, I design to 30 lbs of force for the operator to apply to the sliding tube. If changing from wear pads to rollers does not get your force low enough, you need to make plans for powered extension. Another reason to switch to powered extension is if your system needs to slide while under any significant load.
The most common form of extension is a cylinder. They are inexpensive and pack a lot of force into a small area. Ball screw jacks, rack and pinion systems and cable drives are also popular options.
3. Contact Stress
Contact stress or Hertzian stress is a major concern in sliding joints. This is the stress that the roller (cylinder) exerts on to the tube (flat surface). With a flat wear pad, this calculation is easy; force divided by length times width. However, with a roller is a bit more complicated.
A wrong calculation here can leave divots in the flat surface, making a clunking sound every time the roller passes by.
This calculation is largely a factor of the diameters of the cylinders and the material selected. To get the maximum allowable contact stress use the following two formulas. The formula is based off of two cylinders contacting each other. Since we have a cylinder and a plate, we will make one of the cylinder have a very large radius.
Where:
b is the effective half width
F is the load applied
l is the length (width) that the two cylinder are engaged.
v is the Poisson ration of the materal
E is the Young’s modulus of the materia
d is the diameter of the cylinder. Make one of these very large to simulate a flat surface.
σmax is the maximum contact stress
When using this with other applied loads. The stresses will combine using the square root of the sum of the squares method. You will want to keep the non-contact loads to your standard design factor. When the load is combined with the contact stress, it should be less than the yield strength.
Where Sy is the yield strength of the material, DF is the required design factor, and σp is the principle normal stress of the other loads.
4. Planning for Load Reversal
I once worked on a project where every time the truck went over a speed bump, the lift part of the truck would raise up and then slam down in to the rest. Really loud!
After a lot of research, we found that the scissor structure below the lift was designed to hold the unit up and steady, but there was nothing to secure it in place when stowed. The design assumed that gravity would keep the lift in the proper place.
I share this story because it requires me to think about what happens when gravity is reversed or is 3 to 5 times what it normally is.
Trailers are an excellent example of this load condition. Road fatigue is the major obstacle when designing trailers because they routinely see 4 to 5 times their mass. Not many of us would normally use a design factor of 8:1 or 10:1 to overcome this obstacle.
When planning for load reversals, we may also need to use much higher design factors than normal. This also gives another benefit; a stiffer system. All things are subject to Hooke’s Law. When you push or pull them, they act like a spring.
The amount of energy stored in the spring is subject to the equation above. If I have flimsy sections, my deflection, x, will be much larger and therefore store a lot more energy.
As a result, making the system stiffer reduces energy that can be stored. We want to minimize energy absorption because sound is a form of energy; and the one we are most concerned about in our sliding tube design.
5. Planning for Noise
No one likes to have a noisy machine. As engineers, we can design out many of the of the major sources of noise.
Noise from Roading
Roading is a term for mobile equipment that needs to function on the different road surfaces. A unit can make a lot of noise on one surface say dirt or gravel roads, but on highway can be super quiet.
Running on dirt roads is great source of load reversal. I just mentioned that if we stiffen the system we can minimize the energy stored that may get converted to sound.
Please note that stiffening the system most likely will lead to some weight increase, but it doesn’t need to be a dramatic increase. Make your sections taller rather than adding wall thickness.
Minimize Gaps
In addition to stiffening the sections, we can also minimize gaps. Gaps by definition are places for potential energy to store. Minimizing the gaps is a great way to minimize sound.
If you are using wear pads, design sheet metal shims of differing thickness that can be used so that gaps can be minimized to 0.063″ (1.6 mm) or less.
0.063″ to 0.13″ are typical. Add shims under the wear pads (yellow) to minimize gaps.
If you are using rollers, start off with standard rollers and move to eccentric rollers if you need to. An eccentric roller is a cam follower where the roller and shaft are off center from each other. Rotating the shaft will allow your to increase or decrease the gap in your design.
Often times, you might find that the eccentric roller just doesn’t remove enough of the gap. This is why I always like using roller bearings in conjuncture with slide bearings so they can be shimmed.
Metal to Metal Contact
Metal to metal contact for sliding joints is undesirable especially if there are large reversing loads. Metal on metal not only wears the softer material quickly, it also makes loud noises when contact is made.
The only exception to this is with roller bearings on metal surfaces. While noise can be made on contact, you really do need hard surfaces for bearings to work well. The rolling action will reduce any affects the metal on metal joint will have.
Low Bearing Pressure
Noise is always an area of concern with slide pads. With sliding wear pads, the noise usually comes from a pad that makes light contact.
The Whale
At a previous job, we had an articulating cylinder that had two cylindrical bearings. One of the bearings was directly under the load needed to articulate the cylinder. The other bearing was equal sized but had nearly no load on it.
As a result, the no-load bearing sounded like a irate whale and could be heard from a quarter mile away. No joke…it was loud!
The solution was two part. First, move both bearings laterally a little so that the load was distributed better. Second we narrowed up the no-load bearing so that the pressure increased. The noise vanished!
Recommended Design Pressures
I tell the story so that you think about bearings in terms of the maximum and minimum loads while moving. In general, I look for the maximum contact pressure to be 10% of the tensile strength or a 10:1 design factor. I do this because I assume that only 50% of the pad is actually in contact with the mating surface and then add a 5:1 design factor so that the wear rate is minimal.
I also look for the minimum load on the bearing to be 2% of the tensile strength or 1/5th of the maximum allowable contact load. Keeping this minimum load in mind will increase your chances that noise will not be an issue.
One Trick for Minimizing Area
A popular way to mount wear pads is with flat head socket screws. So if your pressures are just a little bit too low on your wear pad, you can countersink the holes deeper than needed. Not only will it add head clearance for the bolt, it will reduce the area of the pad.
Improper Wear Pad Design
Noise can also come from improper wear pad design. Most design issues have to do with too large a wear pad area as we discussed. The next two leading issues are loose pads and improper fastening.
If your wear pad loosens up, you probably don’t have enough fasteners or they are located improperly on the pad. If you have a lot of noise on a wear pad, make sure that the fasteners holding it are properly tightened.
If the problem insists, look into the design. Start with evaluating if the force, usually shear, on the fasteners is adequate for the job. Look at the retaining method and head clearance. Many times lock washers or thread locking compound my be all that is needed to quiet the joint.
Next look at the chamfers on the slide pad. There should be a lead in chamfer of at least 1/8 inch in the direction of motion. The wear pad should also be longer (in the direction of travel) than it is wide.
Finally, be sure the fasteners are near the perimeter of the wear pad and there are at least 2 fasteners per pad.
6. Planning for Slop
Slop is necessary in every sliding joint. We don’t want our sliding joints binding up from interference when the tolerances are too tight. We also don’t want systems that are so loose that we can’t accurately control or that create noise or vibration every time it moves.
Chances are that you will not be machining every part in the system so we will need to plan our tolerances carefully.
I’ll illustrate why planning for slop in the joint is important by sharing one failure with you. This failure had a deep impact on the way I design sliding joints to this day.
My Critical Error
So this is the area that I made my critical error. As you can imagine, every sliding joint needs some slop or looseness in the system. We need to plan for that. Sliding on rails doesn’t require too much slop, but a tube in tube does (like 1/16″-1/8″.)
My error was that I didn’t plan for this in my tube in tube design. The unit had some “out and down” outriggers where the outrigger had a horizontal tube mounted to the vertical outrigger. The horizontal tube section slid in another horizontal section.
I designed the tube in tube section to have a good amount of slop so that there wouldn’t be any binding. Yea! However, I did not plan for the angle that this horizontal tube would be at when the outrigger was loaded.
When the machine was set up, it looked like the outriggers were broken and about to fail. (However, it was still structurally fine.) Regardless, no operator wants to use a machine that looks like it is already broken.
The cause of this fiasco was that I wanted to minimize the effort by the operator and make the sliding action exactly level. This is somewhat humorous assumption because the operator will likely be setting up on a slope anyway. Once the outrigger was all the way out and started to deploy, the slop in the joint would shift the contact from the cam rollers to the wear pads in the opposite direction.
Result: Looks broken.
What should I have done? Easy, plan for the outrigger tube be horizontal when taking the load; not horizontal when sliding. To keep the same tolerance, I would need make it slide at a slight downhill angle when extending. This solution may now need to be powered or at least have an extension spring to help returning it to the stowed position.
Corrected Design: Left side extends downward. Right side is deployed under load. It looks well designed.
(Interesting side note: the solution to this is the only time I have ever used a 7/16″ screw)
7. Plan for Assembly and Maintenance
This is where most engineers make the big mistakes. Here are the major contributors to assembly and maintenance issues:
Not thinking through how the unit is assembled – Oh boy has this burned me! Tube in tube joints usually have a specific way that they need to be assembled. You need to go through each step in the assembly process one component at a time and insure that each step can be completed. I’ve known many people who can do this in their head. For the rest of us, hiding parts in 3D CAD will do the same job.
Wear pads are difficult to position – Make your wear pads come right up to the edge of the tubes. Not only does this make locating the screw easier because you know it will be flush, but it also increases the overlap of the tubes. Double win!
Not leaving room to tighten fasteners – There is nothing more frustrating that tightening a fastener by flipping a combination wrench over each time or only hearing one click on a socket wrench. Design in more room please!
Reaching inside tube really far – If you need to reach inside a tube more than 18″ to insert a part, something is wrong with your design. I do admit that I have had the occasional design where a bolt spring was needed to install a carriage bolt (see below). It is one thing to reach in to install a bolt, but another to have to hold it during torquing.
Wear and Tear – Debris and rust can prevent you from removing fasteners. I like to avoid using socket head screws where possible because they are notorious for getting stripped because of rust of debris.
Wear pad replacement – Your wear pads may need to be replaced from time to time. As you are assembling this, ask “How many parts need to be removed to swap out the wear pads.” It was always a requirement for me that the wear pads could be replaced by only removing a cylinder pin or other component. I liked to be able to slide the inner tube out the opposite end so that those wear pads could be replaced easily.
Bolt Spring – Insert the bolt into the coiled end and pull it through the hole with the straight end Image courtesy of etrailers.com
Conclusion
Tube in tube sliding joints are more complicated than they appear. There is a lot that goes into making a great sliding joint. This guide should be the first step in identifying critical aspects of these type of joints.
FEA Tip-Pin and Cylinder Modeling for Shorter Runs
I have always said, “There is no such thing as a quick FEA.” In my opinion, FEA is one of the slowest tools in our tool belt. It seems like it would speed things up by not having to do hand calculations, but that is rarely the case.
The truth is that FEA should only be used to verify our design after hand calculations have been completed. (More to come on this in a future article)
FEA run time can be drastically reduced, by making modeling changes to pins and cylinders. These changes allow the removal of contact sets and treating the components as bonded. This can be done while still maintaining accuracy of the results.
We often come upon situations like what is shown below: a simple jib with a hinged pin joint and a cylinder to articulate. Using traditional FEA practices, this can take significant processing time.
With a few simple changes, we can reduce the processing time by nearly 50% without losing accuracy.
Contact sets take so much more time to solve than bonded components
FEA run time can be drastically reduced, by making modeling changes to pins and cylinders. These changes allow the removal of contact sets and treating the components as bonded. This can be done while still maintaining accuracy of the results.
The image above on the left shows how an actual pin would react when loaded. This simulation is achieved by using no penetration contacts in Solidworks Simulation. Contacts take so much more time to solve than welded components (shown on the right). Sadly, the welded analysis is not accurate and this joint can take moment now. Furthermore, there are no gaps: a pin only pushes against one side; this will pull as well.
Don’t you wish there was a way to get accurate FEA results, but run in the time it takes for a welded simulation to run?
Well in some cases you can. Below on the left is the model with contacts. It took 165 seconds to run and gives great results (longer if I used friction in the joint). The model on the right has no contacts and ran in 24 seconds (85% less time).
If you look at the points of interest on the structure and not the pin or cylinder, you really can’t see a difference between the two models.
Really the only striking difference is at the hinge joint where the loads on the clevis are much different.
Let’s see how we can improve your FEA run time.
Cylinders
Unless you are a cylinder designer, you probably don’t care about the internal stresses on the cylinder. (If you are a cylinder designer, don’t use this tip.) As a result we can use this to our advantage.
Cylinders are the first step to minimizing FEA run time. For the example above, there was a 45% reduction in run time just remodeling the cylinder to be a weldment and not use a contact set.
When sizing a cylinder, we generally know what size bore and rod we will need. From these numbers, we can calculate the stress on the pin and determine a proper diameter. (You can use my double shear pin calculator if you like).
How is it Possible?
A cylinder is a two force member so we know which way the forces go. They are either tension or compression. The main exception is a piggyback cylinder that will carry moment along the entire length. (We don’t want any side load on our cylinder either.)
As a result, we can change the end configuration of the rod and bore to simulate the cylinder reactions in one direction. We can also incorporate the pin into the cylinder component reducing our part count from 3 to 1. Most excellent!
On top of that, we can treat the cylinder and what it attaches to as one weldment. This is the main step to reducing FEA run time.
The center section of our cylinder will have a cross section of 1 inch squared. I always use this cross section for a few reasons.
Any rotational deflection will be minimal. A cross section this small does not resist bending on the end very well so it will always be the weaker member and flex first. As a result, the top and bottom faces of the cylinder may have additional tension and compression stresses. (I’ll deal with that in a minute.)
Linear finite element analysis will ignore buckling – Having a really small cross section doesn’t matter in linear analysis. The computer just sees the member as a bunch of points in a matrix. The operator would need to determine if buckling is an issue. Obviously, this won’t be an issue in tension cylinder application.
The stress will equal the force. If you have 25 ksi on the FEA results, you will have 25,000 lb as the cylinder load. This will be a quick way to check if your calculations match your FEA model. If it doesn’t, you will want to check your calculations and your FEA. I always create a small split line section on the sides of the cylinder where I refine the mesh and take my readings. You will want to make the split line section around the neutral axis and half the height of the beam.
How to Model a Male Clevis Cylinder for FEA
1. Model the Main Shaft of the Cylinder
Start with the slot feature and make the slot 1 inch high and the desired length of the cylinder. You can use configurations to have multiple lengths, although you most likely just need the retracted and extended length.
Slot Extrusion
You will then want to extrude it about the midplane to a width of 1 inch.
Split Line Section Sketch
2. Model the Pins
Extrude the pin as shown below for any male clevis type attachment. Notice the lip around the outer 1/4 of the surface. This allows us to have a bonded connection with the bore of the mating hole. This is the change saves us the run time in FEA.
Since our cylinder is used in compression, we have it on the outside of the the model. If the cylinder was in compression, it would be used on the inside.
3. Model the Tube
At this point, the tube can be a simple midplane extrusion with no inside diameter. We are losing some detail here, but we are not concerned with the stresses on the cylinder or pin. We can calculate those by hand easily enough. (Actually, we should have done that before the FEA process began.)
Pin and Tube Dimensions
4. Remove Contact Sets from Assembly
Now that we have our cool cylinder part, we need to insert this and mate it in the model. We also need to remove any contact sets that may be lingering.
5. Measuring Cylinder Force / Stress
After the analysis has run, right click on the stress plot and select “List Selected” from the pop-out menu.
Then select the two split lines on the side of the cylinder, click update and look at the average stress. If your cylinder shown signs of bending, as is the case below, this number will be a little higher than expected. If this is an issue, you can simply make the split line section narrower to be closer to the neutral axis.
Modeling a Cylinder with a Female Clevis
1. Start with the Pins
The female clevis is constructed differently so we need to approach it differently. With any cylinder, we are very concerned about the length. This is easy to control in the male cylinder with the slot extrusion first. With the female version, it is easier to start off with the pins an work our way to the center.
Start by modeling the sketch above, adjusting the outer diameter to your bore, and extruding to the effective length of the pin.
2. Extrude the Shaft of the Cylinder
Drawing a ‘I’ section on (usually) the top plane, creates the shaft of the cylinder. We will want to make the thickness of the shaft and flange of the ‘I’ all one inch. We will extrude one inch so that we keep the shaft at 1 square inch in cross section.
The ends of the beam are shown 1.75 inches away from the center of the pin. This length is arbitrary. We want to keep it as short as possible, but we don’t want it to interfere with the mating components.
Two final things to note is that the width of the flange will be coincident with the end of the pins and the shaft will be symmetric with the length of the pin.
3. Join the Components.
The next step is to join all the individual bodies together. Sketch two rectangles on the top of the ‘I’ section to the centerline of the pin. Add a dimension in between the rectangles to hold the inner distance of the clevis.
4. Add Your Split Line for Load Monitoring
The final step is to add a split line feature so that you can quickly monitor the load. This should be done on the sides around the neutral axis as shown above.
Completed Female Clevis Cylinder with Split Line Section for Load Monitoring
Pins
Pins are more complicated. Rarely will a pin give you accurate results so I issue the following warning:
Warning – Rotating pins will lower the accuracy of the results when used without contacts. This also does not work if the the load is unequal on each side (i.e. a side load) . When in doubt, don’t use this method.
With that said, this is still a viable option if your area of concern is somewhere other than this joint. If you are concerned about this joint, this analysis technique will not work.
Following this process can help you determine if can cut your FEA run time by a total 85%, in this example. (An additional 74% after the welded cylinder is applied.)
Calculate, by hand, the force, direction of the force and stresses on clevis before running FEA.
Run the model with contacts at least once to get an idea of what the stress should look like in this area. Record the run time.
Look at the stress flow and magnitudes to see if this is an area or concern. If it is, stop at this point. You will need to use contact sets for the model. If it is not an area of concern, proceed to the following steps.
Interpret the stress to see which way the stress should flow through the pin. In the figure below, the pin has three nearly vertical lines. We would initially make our pin have the contact surface be perpendicular with this which is about 15° from horizontal. (Using our forces in Step 1 will also give us an idea of the angle needed). We will need to have the contact at the bottom on the jib arm clevis and top on the vertical tube clevis. (If I remove the pin, the jib arm would go up and to the right.)
Model a pin with reliefs in it and orient accordingly.
Run the analysis and adjust the pin accordingly.
Using Contacts
Modeling the Pin
Similar to the cylinder, we will model the pin with reliefs in it so that it only contacts where it should according to your hand calculations.
1. Extrude the Pin
Make a simple cylindrical midplane extrusion for the nominal diameter of the pin and set the length to the effective length of the joint (no extra length for clearance). The midplane extrusion will ease the rest of the process and usually give a great way to mate the pin in place.
2. Add a Center Relief
Make a sketch on the midplane of the pin two concentric circles 1/16″ (1.6mm) apart. Add the lines shown and make them coincident to the center of the circle. Add a 90° dimension and make one set of points vertical. This causes the cut to be symmetric about the top plane. This will help us in mating the pin in the model.
Center Relief Cut
3. Add the Outer Relief and Mirror
Make a similar cut as above from the end of the pin to the surface of the center relief. This cut should be 180° from the center relief cut. Once complete, mirror it about the midplane.
Pin with Outer Relief. (Left) Before Mirror, (Right) After Mirror
4. Inserting the Pin into the Model
After the modeling is complete, you can replace the existing pin with it. We will mate it at 15° from horizontal as indicated from the stress lines. Remove any left over contact sets and run the analysis.
Pin Inserted at 15° Below HorizontalFEA at 15° Below Horizontal
You can see here that the stresses are much higher than the solution with contacts. This is because the pin is installed at the wrong angle. Don’t get too caught up in this because we aren’t looking for accuracy in this location anyway.
However to illustrate what an acceptable angle is, I have rotated the pin to 60° below horizontal and rerun.
Once again, we are not looking for accuracy in this joint. If you need accuracy, use a contact set. Also, don’t spend a lot of time trying to figure out what the “right” angle is. On short run models, under 10 minutes, you have eaten up any time savings by screwing with the pin angle more than once.
In Summary
FEA run times are often excessive and we should be looking for ways to simplify our modeling. Modeling cylinders and sometimes pins as weldment components instead of pivoting items needing contact sets, FEA run time can be minimized significantly.
Model
Run Time
Reduction
Contact Sets on Pin and Cylinder
165 s
–
Bonded Cylinder Contact Set on Pin
91 s
44.8%
Pin and Cylinder Bonded
24 s
85.4%
By using these two concepts, we have been able to reduce the FEA run time from 192 seconds to 24 seconds. What a time savings!
As an engineer, there are many times where designing a beam by stress alone just isn’t good enough. Walkways and decks are designed for deflection because the the human mind feels the movement and if excessive and if the movement is too much, it concludes the structure is unsafe.
Another example of designing for deflection is an airplane wing. In commercial jets, the wings are very stiff compared to those of cargo military planes. No one wants to look outside the window and see the wing bouncing 10 to 15 feet up and down in a thunderstorm. You would conclude that at any moment the wings may break right off.
To decrease deflection for a beam you can: decrease the load, moment or length of the beam; change the support types or location; add more supports; increase the are moment of inertia of the modulus of elasticity or add other beams to share the load.
Designing for deflection rather that stress quite necessary sometimes. The rules of thumb when designing a beam for deflection are:
The live and dead load deflection cannot exceed L / 240 and
The live load deflection cannot exceed L / 360
You can use my ultimate beam calculator to help. Let’s explore how each of these will change the deflection of the beam.
Decrease the Load / Moment
This is clearly the easiest way to decrease deflection, but most likely not probable. If I am designing a single person walkway, I can’t easily lower my weight (although I do need to lose a few pounds). Besides there are many standards that dictate required live and dead loads. Most likely, this is a non-starter.
This option is also quite obvious, but often times impossible. You probably already optimized this in your design. If you were building a bridge, you want the piles to be on solid ground but if that isn’t possible, you want them to be in shallow water.
If you can move your beam supports, consider having one or both of the ends cantilevered. More on this a little later.
Maybe moving the supports closer is possible
Change the End Supports
Changing the end supports will allow you to increase the beam’s stiffness without modifying the beams section. Here is the hierarchy of supports with their relative stiffness to a cantilevered beam.
Fixed at each end (48x)
Fixed at one end, supported at other (23x)
Supported both ends (9.6x)
Fixed at one end, guided at other (3x)
Cantilevered at one end (1x)
In each case, you can see that the benefit of moving up one rung the support hierarchy makes the same beam nearly three times stiffer. If you have a cantilever beam, adding a support under the free end will change the stiffness to a fixed and supported beam increasing the stiffness 23x!
The most common beam support is supported at both sides also known as simply supported. This beam is already fairly stiff and easy to construct. However, if we make one beam span three supports, we have actually changed the center portion to a nearly fixed support. I say nearly fixed because the support can still rotate at the center position. However, this support is still attached to the other ends so it must take some moment at the center support. If this maximum load on the beam is symmetric about the center support, we can assume the joint is fixed in the center. This will make our same beam 2.4 times stiffer than it was before. This is a small change that boasts great results.
Beam with three supports
Add a Cantilevered Section on the End(s)
This is a way to keep the same total beam length while decreasing the distance between the supports. From the hierarchy listed above, a simply supported beam is 9.6 times more stiff than a cantilevered beam this means that I could actually cantilever the beam off one end by 10.4% (1 / 9.6)
Adding a cantilever to one end of a beam
For example, if I had a 100 inch simply supported beam, I could move the support on one end in roughly 10% of the total length. This not only reduces the deflection by 31% (results depend on materials used and cross section), but also when used in decking gives the feeling of the deck stretching past where it should. A great feeling for a deck owner.
You can do this on both ends of your beam if necessary.
Looking at the generic beam formula below, we can see that if the moment stays the same, only the area moment of inertia. I, and the modulus of elasticity, E, can be modified to reduce deflection, v. In this section, we will discuss the area moment of inertia.
General Form of the Beam Equation
The area moment of inertia is entirely based on the shape of the cross section. As the cross section increases, so does the moment of inertia. In fact for a rectangle, if you double the height, you will quadruple the moment of inertia. However, if you double the width, you only double the moment of inertia.
Here’s what to do with the following structural shapes
Round Tubing or Pipe
With round tubing or pipe, the easy solution is to thicken the wall. For example, 1/4″ thick tube becomes 3/8″ thick or schedule 40 changes to schedule 80 pipe. You will only see moderate increases in stiffness as the wall thickens. This may be enough, but your section is becoming heavier. At some point the additional weight may actually increase deflection.
The best solution is to increase the outside diameter of the tube or pipe and keep the original wall thickness. If this is not possible, consider switching to a square tube.
Square Tubing
Square tubing is very similar to round tubing, but it does have the advantage that all the material is on the outer edge and is great for bending in both the horizontal and vertical directions (assuming a horizontal beam). With this in mind, be sure that the flat surface on the tube is oriented with the largest moment on the tube. The tube isn’t as strong when it is loaded as a diamond.
Non-rotated vs rotated square tube
Angles
Angles just don’t make good beams. If you are having troubles with your angle deflecting too much, consider changing it to a different shape. Any shape is better. Just do it. You’ll thank me.
Wide Flange Beams
Wide flange beams offer a wide variety of solutions for your design. There are so many sections to choose from and often you don’t need to increase your height to make a dramatic change in strength.
Beam
Moment of Inertia (in^4)
Increase
Weight Compared to W16 x 31
W16 x 31
301
–
–
W16 x 45
586
1.94
1.45
W16 x 67
954
3.16
2.16
From the table above, you can see that going from a W16 x 31 to a W16 x 45 doubles the stiffness while only increasing the weight 45%. Going to a W16 x 67 doubles the weight and triples the stiffness.
If your wide flange beam sees loads on the weak axis, consider boxing the sides in. Generally speaking, the plates don’t need to be very think to make a big impact.
Increase the Modulus of Elasticity
Increasing the modulus of elasticity is difficult to do in most cases. Pretty much the only way to increase this is to change the material. If you are already using steel, you’re on the top of the food chain; there is no more room to improve.
There is a lot more room to in the realm of plastics and non-steel metals. Often changing from a standard plastic to fiber reinforced plastics, fiber glass or carbon fiber is a good move.
Below is a list of common items and their modulus of elasticity sorted from highest to lowest. If you need to minimize deflection, consider a material higher up on this list.
Adding more beams to carry the load can be an effective way of minimizing deflection. If we have one beam and add a second, our deflection will be cut in half. Excellent!
However, if we have 2 beams and go to three, we may end up with the same deflection if you don’t plan your beam locations right. Assuming a distributed load across the width of the beams, the center beam may take 1/2 of the load and the outer beams only take 1/4 of the load each. The figure below illustrates this point and the equations give the load on each beam.
Non-equally loaded beam with center support
Where w is the distributed load, usually in force per area (N/m^2 or psf), W is the width of the structure and n is the number of beams.
The center beam is responsible for 18″ of the load width and the ends are only taking 9″ of the load. This is why adding another beam in this manner is counterproductive.
Now, to get each beam carrying an equal part of the load, we need to move the outer beams in so that the distance from the center of the outer beams to the end is half the distance between the beams. The figure below shows the proper relation.
Equally loaded beams
This works because each section of beam is responsible for 6 inches of the load to each side.
The next time you drive under a concrete bridge, look and see how the girders are spaced.
There are many ways to minimize the deflection on a beam. Looking at the loads, supports, section properties and the material will allow you to see what options are available to stiffen your beam.
Overheating: The Hidden Danger in Pressure Compensated Hydraulics
On a recent project, there was a 25 horsepower motor running a torque limited piston pump. When we were doing performance testing, everything worked out fine. As soon as I left, the customer was complaining about excessive heat generation leading to downtime waiting for the oil to cool.
At first, I thought that a relief valve may be set below the compensator pressure, but a quick check showed they were operating correctly. So I did some research.
The problem wasn’t clear until I talked with the pump manufacturer. In order to keep a pressure compensated pump cool, the oil needs to be circulated internally. Depending on the manufacturer, 1/4 of the flow may be dumped back to tank to keep the pump cool.
Pressure compensated hydraulic systems tend to overheat because oil is continually circulated to keep the pump cool. The higher the standby pressure, the more heat created. Adding heat exchangers, shutting the pump down and lowering or having adjustable stand by pressure can reduce the heat generated.
So you have spent the extra money to get a piston pump, but do you know that there is a hidden danger in built in to these pumps? Let’s explore the danger
The Cause of Heat
It turns out that pressure compensated systems are always moving oil, even when in standby. I found out that roughly 3 to 4 gpm were being dumped back to tank through the pump’s case drain at the compensator pressure. This was nearly 7 horsepower that was wasted.
This situation was not detected in testing, because we ran back to back tests with no idle time in between. Once the idle time was added in, we discovered that the oil temperature rose around 1-2 degrees per minute. An impressive feat on 100 gallons of hydraulic oil.
There are several ways to minimize the heat generation with a pressure compensated hydraulic system
Add a heat exchanger
Minimize idle time
Shut the system off
Lower the compensator pressure
Adjustable the compensator pressure
Add a Heat Exchanger
Adding a heat exchanger is a very obvious solution. These are usually forced air radiators made for hydraulics that are installed on the return line or the case drain line.
In an industrial application, an 8 hp heat exchanger is going to run around $1000 (in 2019). That doesn’t include the cost of the hoses or an electrican to wire the fans. Mobile (12 VDC) applications are less expensive and easier to wire yourself.
But as an engineer you should be asking yourself, “Why am I generating all this power just to heat the shop? That extra heat is going to make working in the summer excruciating.” All that an it is wasteful as well.
If we assume that we have 7 hp of wasted power from our pump during idle time, that is 5.2 kWh of energy. At 12 cents per kWh, that is $0.63 / hr of idle time.
That is a super expensive waste of energy!
If the only reason you are adding a heat exchanger is to reject idle time heat generation, there are many other options which we will explore below. Don’t let the simplicity of the a heat exchanger solution be where you stop. Keep reading.
Minimize Idle Time
As an engineer, the first step should always be fully diagnosing the root cause and not just masking the symptom. If you notice excessive idle time, make inquiries as to why the machine idles so much. Is an operator waiting on another process? Is it breaktime? They are many reasons for high idle time.
If the idle time can be modified by a process change or other external change, do that. However, don’t let that be your only change. People and processes aren’t perfect so expect those types of changes to occasionally fail.
Shut the System Down
This one is pretty self explanatory. If the system doesn’t need to be on, shut it down. If the system isn’t running, it can’t create heat. In fact, it has the opportunity to reject heat out of the system. Win-win!
One thing that we want to watch out for is turning the motor on and off too much. Motor startup is a significant source of wear on the motor so we want to minimize the number of startups.
Luckily, pressure compensated systems will start in a loaded condition. There should be no (or little) pressure on the outlet and compensator. This means that when starting the motor, it won’t be anywhere near fully loaded. Since there is no pressure, it will take 1-3 seconds for the pump to produce enough pressure to load up the compensator. This will usually be long enough to minimize startup loads on the motor.
If the machine is PLC controlled, adding a timer is easy to do when the machine is idle. This will be a good back up to the case where an operator accidentally leaves the system on when it is break time.
In the machine discussed above, we added a 2 minute timer for periods when there were no outputs given to any function. This was a great protection from heat generation, plus it was a signal to the operator that he or she was taking too long. Yes, it also had the side effect of increased production.
If excessive motor startup is a real concern, you may want to add a restart delay. This is common in HVAC systems where it is common to see a 5 minute ‘compressor delay’. This delay probably adds many hours of life to your HVAC system.
The same can be done with your system. Maybe 5 minutes is excessive, but 30 to 60 seconds may be just enough to lengthen the motor’s life.
Lower the Compensator Pressure
In some hydraulic systems, you just don’t need the system pressure you designed for. As a good designer, you have calculated your pressures and flows for less than what is available. As a result, you can reduce the standby pressure, but only minimally.
I say minimally, because there isn’t a drastic reduction in power with this one. However, you know your machine better than I do, so maybe there is more energy savings here.
Variable Compensator Pressures
This option has many possibilities and the best results for improving effiency. We will explore the basic options:
Adjustable compensator relief valve
Multiple preset compensator relief valves
Dump the flow to tank
Adjustable Compensator Relief Valve
This option is the most expensive and most efficient. By using an electro-proportional relief valve (DO3 P to T relief valve for industrial applications), you can set the compensator pressure for exactly what you need for the current function. As the functions change, the compensator pressure changes.
This is the most expensive option because your PLC system is going to have to output an analog signal (usually 0 – 10VDC) to control the electro-proportional relief valve (also expensive). As a good designer, you will also want a pressure sensor to provide feedback on the system.
However, this system is fully customizable and can act similiar to a load sensing mobile system. Through careful programming, you can tailor your pressure setting to what that function needs at any particular time.
This function would also allow you to gradually change pressures from function to function thus preventing hose jumping.
Be cautious, the programming can get very complicated. It may not seem to be a big deal now, but will cause headaches in years to come when you or others will need to service the machine.
Multiple Preset Compensator Relief Valve
This is a much simpler version of the adjustable compensator option above. In this scenario, we would have one or more compensator relief valves switched on or off by non-proportional solenoid valves.
In this system, there would be one relief valve (main relief below) tied directly to the compensator and other relief valves are separated from the pressure line by 2 position, 2 way, normally closed solenoid operated valve. The main valve must be set at the maximum desired pressure so that if all else fails, the system will have a direct path of pressure control. The other valves can be activated, one at a time, to control the pressure for certain pressures.
This system cost is also reduced from the adjustable relief valve option because it eliminates the needed analog control system and extra programming for the PLC.
Additionally, the system can be made to look quite neat as well. Having a multisection DO3 manifold with the pressure port connected to the compensator will provide the foundation. Often, you can get the main relief valve already incorporated into the manifold which is a big bonus. You can then add solenoid valves on as the first row. On top of those valves you can add the individual relief valves.
If none of the sections are energized, the pump will create the maximum pressure which is set in the manifold relief valve. If one or more sections are activated, the pump will create pressure to the lowest set active pressure. In the schematic above, you can adjust the compensator pressure to 600 psi, 1200 psi, 2200 psi or 2750 psi depending on which sections are activated.
With this setup, you can customize the needed pressure while saving money and preventing heat generation.
Dump the Flow to Tank
This can be a subset of several other options. If your system idles for long periods of time, you can just have a 2 position, 2 way, normally closed solenoid valve dump the pressure to tank. This will destroke the pump and not create any heat.
This is a better option than having the motor turn off because it will reduce the number of starts and stops.
Another option on this is to couple it with a timer so that if there is no demand for the system hydraulics, the solenoid will activate and the pressure will be reduced. When demand for higher pressures is needed, the PLC will deactivate this solenoid.
Which one did I choose?
I actually chose two of these solutions. First, I put a two minute timer on when the system is in normal standby. There is also a 25 minute timer when the system is in the cutting mode. At the 25 minute cycle, only 500 psi is needed to operate a hydraulic motor and control the travel of a saw.
In cutting mode, I also reduced the standby pressure from 2750 psi to 500 psi reducing the needed power by 82%. Sweet! I accomplished this by adding a second compensator relief valve that is activated by a 2 position 3 way valve.
Conclusion
Pressure compensated systems are generally more efficient and with a torque limiter they will give you the best performance of any other hydraulic system. Unfortunately, they do have the drawback of heat generation when in standby mode. If the solutions above are applied, you can often eliminate the need for a heat exchanger.
Selecting the Best Directional Control Valve Center Position
