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The Best 4 Ways to Improve Torsional Beam Performance
I recently stayed at a very nice hotel and out at the pool there were some plastic rocking chairs. I sat in one and rocked for a few minutes and noticed something odd. In addition to the chair rocking, there was a vibration where one side of the chair was leading the other.
The cause of this was obvious; the floor was uneven. This sparked my interest because I had never noticed this in any other, mainly wooden, rocking chair. Not being content, I had my wife sit in the rocking chair next to me and she noticed the vibration as well.
Even on vacation, I cannot turn off my mind so I flipped the chair over and immediately noticed what caused the issue. The sections that made up the chair were open sections in the shape of a U and would deflect much more than an equivalent wooden rocker when in torsion. That extra deflection, allowed the vibration I noticed to occur. In this article, I will discuss multiple ways analyze and improve torsional resistance in structures so that you will design a better rocking chair.
In order to design a better section for torsional deflection consider using closed sections like bars or tubes; avoid plates and structural shapes. You can also box in open sections, thicken walls and apply bracing.
1. Open vs Closed Sections
One great challenge of engineering is designing structures for torsional loading. This can be an issue for two reasons: first, calculating the stress in open sections can be rather difficult. Second, the deflection of a section can be excessive and ambiguous to calculate.
Let’s examine why designing for torsional loads are much harder than bending. In the, I beam shown, tension and compressive stresses flow through the top and bottom members. The deflection will be very predictable since it is governed by the equation:
Where M is the moment applied, E is the Young’s modulus, I is the Area moment of inertia and v’’ is the second derivative of the deflection. Using this equation, you can use your calculus skills to integrate and setup your boundary conditions etc. I prefer to look these up in a table like everyone else. My reference of preference is Blodgett’s Design of Welded Structures.
Now, if we take the same I-beam and apply a torsional load to it, logically we would expect it to have a large amount of deflection. But why? The reason for this is that there is nowhere for the torsional stress to flow. In bending, the web of the beam takes the shear load in between them. If you remember the first few days of your Mechanics of Materials class, you will recall that shear stress is maximum at 45° from the longitudinal axis where it essentially becomes a normal stress.
Consider applying torsional stress to the ideal section, a tube. This is because the torsional stress has some where to flow. Imagine taking a tube and cutting it at a 45° angle from its axis. (Think of a candy cane stripe.) Now flatten it out. What do you have? It is a flat bar. Since shear stress is normal stress offset by 45°, normal stress flows freely through the flat bar.
With torsional loading, there are two types of sections, open and closed. An I-beam is an example of an open section and the tube is a closed section. Obviously there can be combinations and modified versions of both. Closed sections are preferable for torsional loading because there is a very clear path for the shear stress to flow in. The generic closed section torsional formula is based on the “average enclosed area.” The larger the enclosed area, the better the torsional resistance. There are trade-offs with using a closed section. In the table below, three sections with equal areas are compared. You can see that you can shape the material to be good in bending or torsion, but you will have to compromise to get one that is good in both. An I-beam is great in bending and conversely, the round tube is great in torsion.
You can also see that the rectangular tube is a decent compromise and is readily available. From quick inspection, you can see that material had to be taken from the flanges of the W beam to form a second vertical that creates the wonderful closed section.
When you can use a closed section, do so. But what happens when you just have to use an open section. Two very important questions come to mind. How much will it twist? How do I make this section better?
Good news! Both can be answered.
2. Box in Portions of Open Sections
For the former question, I wanted to point out the excellent work of Omer Blodgett in his book, “Design of Weldments” put out by Lincoln Electric (Section 3.6). If you do not own a copy of this, get one. It is a priceless tool every mechanical engineer should have. In the torsion section of the book, Blodgett describes how torsional resistance can be calculated using some formulas. He then correlates the calculated deflections with real deflections. For most open sections you find, you can use his torsional resistance method to calculate the stiffness of your section by combining smaller components that he provides information on. For example, Blodgett describes an I-beam as three flat plates. From these equations, we can easily estimate the twist and see what changes will make it better (or worse). Since this is an empirical principle, it is not 100% accurate, but will give a reasonable representation.
The latter question can be answered by understanding that closed sections don’t have to be closed the entire way. Let me explain by making a parallel to a section in bending. Going back to I-beam example. If I put a small hole (Figure 1) in the web of the beam, the shear stress will simply flow around it. It makes a stress concentration. If I make the hole a slot it (Figure 2), there may be more of a disruption in the flow, but the beams is still going to work well in bending. Now, if I make the slot longer (Figure 3), at some slot length, the whole I beam section will stop functioning as a unit. This will result in bending stresses in the flanges (not just tension or compression) and the section is no longer capable of working as intended.
Figure 1
Figure 2
3. Apply Bracing to Open Sections
The same is true in torsion, having a closed section for part of the way will improve the rigidity of the beam. Let’s say that our I-beam is cantilevered with an offset vertical load on the opposite end. On the mounted end, it is boxed in for the first 10%. The boxed end stiffens the entire length (not as much as a fully boxed section) because it forces the flanges to bend upon their strong axis. Since torsion flows in a constant direction, the flanges will bend in opposite directions. In figure 4, you can imagine a torsional load bending the top flange away from us and the bottom flange towards us. Figures 5 and 6 show alternate methods of boxing in a partial section.
Figure 4 – Boxed in end section improves torsional rigidity by forcing the flanges to bend as well as twist.
Figure 5
Figure 6
What I want you to understand is this: a section doesn’t have to be perfect or uniform the entire length to do what it needs to. A slot in an I-Beam is acceptable for bending and a semi-boxed in section used in torsion can work as well. I do want to point out that some of these methods may create rather larger stress concentrations where the sections change. Be aware of this and be sure to taper plates to alleviate large stress concentrations.
4. Increasing the Thickness
As a last resort, increasing the thickness of a plate will increase torsional stiffness. This comes at a large weight penalty so use this sparingly. Please note that the largest shear stress on a plate will occur at the center of the longest side. You may be able to add more material by welding a thinner plate in this location. This will minimize some of the added weight.
Conclusion
Designing for torsion can be daunting, but with practice, your mind will start to breakdown the sections. It will first happen by spotting open and closed sections. Then it will break open sections into calculable components. Pretty soon, you will love the creativity you can use in open section design. Remember to ask yourself: How does the stress flow at 45°. Can I enclose this section? How about part of it? It isn’t as tough as it seems once you know what to look for.
Now go design your better rocking chair!
The Best Way to Design for Ergonomics
What is “ergonomics?” Simply put, ergonomics is the study of people’s efficiency in their working environment.
The best way to design a machine for ergonomics is to put yourself in the roles that the people interface with the machine. Some are obvious like the operator, but others are not. Maintenance is one that is often overlooked
As engineers, we realize that most things we design will interface with human beings at some point. In other words, people will be using the products we develop. How easily, safely and efficiently will people be able to use our products? For the electrical engineer it might be creating access to a touch screen computer that is “user friendly” for all. For the mechanical engineer, it may be allowing enough access for people to service parts located inside a tube.
Humans come in all sorts of shapes and sizes, so designing for all of them is definitely a challenge and one to consider carefully. For example, designing a computer touch screen interface is easy for a small person with petite fingers to use. However, when a person with larger fingers tries to use the same system, the wrong keys are continually pushed. Have you experienced this? Think about how frustrating it must be for a 6-foot tall male to text on any small scale device.
Safety is one of the key benefits to excellent ergonomics. If the operator is not forced to work in awkward positions and is performing the job comfortably, increased safety is ensured. Awkward positions can drain one physically and mentally, and can even lead to a loss of balance resulting in injury.
Increased productivity is another benefit to good ergonomics. When the operator is able to perform a job comfortably without becoming fatigued, he can usually work longer requiring fewer breaks.
When designing with ergonomics in mind, it’s helpful to know all about the human body. There are many good reference books out there that chart all sorts of useful information about reach, body strength and comfort level. For example, did you know that placing high impact, high load jobs at waist level allows the operator to leverage the natural strength of their body? Or the grip strength of a person’s hand is cut by more than half when the wrists are bent at 90 degrees towards each other? Facts like these are all readily available. See my resources page for recommended resources.
The Ergonomics of a Log Splitter
Now, fellow engineer, let’s get our hands dirty. For the remainder of this article, I will be doing a case study on my log splitter to see how ergonomics plays into the design. As you can see, my log splitter is in need of an ergonomic upgrade! Let’s look at loading a large and heavy log. The operator (me) would need to stand up and rotate the jib into position above the log. This is an unpowered manual process and there isn’t a good location to push between the shoulders and waist. In this figure you can see that I can only grab the cylinder rod or lifting chain. These are both bad choices because they move. Adding a handle bar could resolve this concern ergonomically.
The next ergonomic issue is placement. When the load is on the left side of the machine (standing at tongue looking at axle), the operator is required to duck under the jib or in between the jib and cylinder to operate the jib cylinder. Both of these options are dangerous because the operator is bent over and at risk for injury or worse. To eliminate this, there are three good options.
First, the valve could be relocated to a better position. Secondly, it is possible to add another control valve could so that operation from both sides is easy. A third option is to add a longer throw to the lever as shown. This is an easier idea to implement, but the valve may not be designed to withstand the added load of the handle. This could manifest itself in the valve centering spring failure caused by road travel fatigue.
Once the log is in place, the normal working area can be considered. A brief inspection shows that sitting is the proper body posture for this machine. For good ergonomic design, the log should be able to be handled from this sitting position. When making the first cut of a large log, if you aren’t paying attention, one half can fall on the other side of the machine. This requires the operator to bend over the machine and pick it up putting undue stress on your back. This is an obvious ergonomic and safety concern. Perhaps a shelf could be added to the machine to support the wood. If both sides of the machine are to be used, the designer should make this part removable, or design it to swing or slide into position.
Notice the sitting stance of the operator when using the log splitter. In order to operate the valve, and handle the log coming off the knife, a very wide arm span is required. Even for a tall person, this would lead to increased fatigue. Moving the valve closer to the operator would mitigate this issue. The picture below shows the operator operating the valve with a lever. As a result, he is able to move closer to the knife and reach the out-feed table with a much narrower stance. The operator can easily reach for a log (to his left or across the machine), position it in front of the knife, split the wood using the improved lever all while controlling the log with one hand. This positioning should lead to decreased fatigue as well as increased productivity.
The gathering of fresh wood up to the log splitter is a mixed ergonomic issue. There can only be so much wood stacked around the machine for the operator to grab while sitting. At some point, the operator will need to stand up and bring more material to split. The benefit of this ergonomically is that it requires the operator to move around, stretch and take a break. However, the operator may have just gotten into a rhythm and has to be interrupted to acquire more wood to split. A simple solution is to have a second person bring wood to the operator.
The final ergonomic (and safety issue) with the log splitter involves the exhaust system on the engine. This engine has the exhaust pointed right to where the operator would sit on this side. The fumes are too noxious to operate from this side. Perhaps designing another exhaust configuration to point this in another direction would work. (Be sure to prevent the exhaust from being sucked right back into the air intake. This would lead to poor performance.) Another alternative is to add a baffle that forces the exhaust to go in another direction. I will be looking into this as an option for my log splitter.
When designing for ergonomics, the following is important to keep in mind. There are many areas that can be easily identified looking at a 3D model. However, some areas of ergonomic improvement can’t often be seen until the prototype is made. This may be far too late to change problem areas! Building a mockup out of cardboard is one of the best ways to foresee ergonomic issues. I believe that cardboard is one of the best materials for this because it is cheap, readily available and can be easily formed into a variety of shapes.
Here are 10 basic ergonomic questions that can be answered during the design phase of the project. Precious time and money can be saved if these questions are answered early on. You don’t want to find yourself launching a new product that is unsellable.
- What is the basic flow of material through the machine?
- When does the operator have to interface with the material?
- What position is the operator in during these times?
- Are there times when the operator has to operate two or more functions? Can these be eliminated or reduced?
- Can the operator see the effect of what is being controlled? Can mirrors, windows, cameras, etc be added to eliminate this?
- Does the operator wear gloves? Do the controls allow easy access with gloves on?
- Can a touch screen computer work with gloves on?
- What routine maintenance needs to be done such as lubrication? Is there access to these areas?
- Are access holes large enough for an operator wearing gloves?
- Is the area properly lit?
- If the apparatus is to be used at night, is the lighting too bright or the wrong color of light? Will the light ruin the operator’s night vision?
In conclusion, designing for ergonomics is a necessary and challenging part of the design. With the simple processes outlined in this article, you can be proactive when designing with ergonomics in mind.
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Now let’s hear from Corey Rasmussen, owner and managing director of the Mentored Engineer.
A Simple Guide to Designing Structural Pivot Pins that Last
Throughout my career I have had to apply thousands of pivoting pins. All have their unique loads and design criteria. They have ranged from pins that don’t rotate to pins that rotate on three surfaces and have loading in multiple directions.
After much research and weighing many options, I have settled on one type of design. My go to choice for a pivot pin is Turned Ground and Polished (TGP) Pre-Chromed Stressproof (ASTM A311 Class B). It has 100 ksi yield strength, good ductility, weldable and can be hardened to about 130 ksi. This will have a a welded lug for rotation lock on one end and a snap ring groove on the other.
The material and its hardness, surface finish and roughness need to be considered when designing a pivot pin. It is also critical how the pin is retained; using double retention with a rotational lock. Finally, you must consider how to assemble and disassemble the joint. A “bullet” guide can help here.
Let’s look into these components a bit deeper.
Material
When choosing a material, three main things need to be considered: strength, hardness and surface finish. Each of these play a critical role in how the pin will perform in the application.
Strength
For pins, you want the material to be strong. A strong pin will reduce the required diameter leading to lower weight and easier installation.
Hardness
The pin must also be hard or at least have the opportunity to be hardened. A hard pin will resist gouging, galling and indentation from roller or ball bearings. This means that carbon percentage (last 2 digits of the alloy number) are going to be higher (over 40 ie 1045 or 1144). If this is the case, you are going to have watch out for the material’s weldability. This will require special welding wire and possibility a pre-heat and controlled cool down. If you pin isn’t hard enough, look at induction hardening. This is a process where material is heated by electromagnetic induction and then quickly quenched. It increases the martensitic composition at the surface leading to increased hardness. If designing for a non-pressed spherical bearing, be sure to induction harden. In this case, the bearing will rotate between the pin and the ID of the spherical bearing. Hardening the pin will prevent galling.
Surface Roughness
Surface finish is a way of measuring how rough a surface is. For most applications with pins, you want a material to be smooth with surface finishes below 16Ra for most applications. Using Turned, Ground and Polished (TGP) or Drawn, Ground and Polished (DGP) materials give a tightly toleranced OD with a very smooth finish.
Surface Finish
Pins need coatings to prevent them from rusting. A pin that has rusted into place is no fun to take out. Keep in mind that a well plated pin can rust to an unfinished bore. Be sure to minimize this by using an anti-seize compound upon assembly and repair. In my career, I have taken out many pins with an air hammer or a cutting torch. Not fun. I will discuss some of the most common finishes.
Zinc plating
Also known as white zinc, this is probably one of the most common finishes out there. It is technically known as trivalent chrome zinc plating. The zinc plating does very little for corrosion protection and chrome is added to provide nearly about 30 hours of salt spray resistance. This plating is weak and I don’t recommend it for outdoor use.
Yellow Zinc plating
Probably one of the most common finishes out there. It is technically known as hexavalent chrome zinc plating. The zinc plating does very little for corrosion protection and chrome is added to provide nearly 100 hours of salt spray resistance. Unfortunately, hexavalent chrome has landed on RoHS’s (reduction of hazardous substances) list and is quickly becoming a thing of the past. You may remember that hexavalent chrome was what the movie Erin Brockiovich was based on. The finish is also soft and can scratch off easily.
This is a great plating and I recommend it.
Zinc phosphate plating
This is a good method of plating steel. The main drawbacks are that it cracks easily and cannot be hammered which can cause installation issues. Also, the salt spray rating isn’t great and lasts about as long as powder coating does. I recommend to stay away from this for outdoor use.
Hard chrome
This is my personal favorite. Chrome offers great corrosion protection and a very smooth and hard surface. It can be bought as pre-chromed bar and easy use in several materials.
Nitrocarborization
Also known as nitriding, this finish is applied by allowing chemicals to soak in to the surface of the steel. The process is not like electroplating in that the chemicals can get into every crack and crevice of the pin. Since it is a soaking process, it does not build thickness to the part, but impregnates it below the surface. Also, it leaves a nice black finish which is a thin oxidation film. As the pin wears on a bearing, this layer will flake off leaving a chrome like finish. It also hardens the surface a little. The main drawback to using nitrocarborization is the stress relieving that occurs during the soaking process. The process generally reduces the yield strength by about 15%. If this wasn’t the case, every pin I spec would have this finish. When deciding to use this process, be sure to have the material tested for yield strength, hardness and elongation. Use a coated and uncoated specimen to compare.
I recommend this for applications where good surface finish and wear is critical, but strength is not. Many times, you can make your pins larger in order to used this surface finish.
Pin Retention
The next thing to focus on is pin retention and the first question to ask if whether or not the pin will rotate in normal operations. I don’t know why, but if it can rotate, it will and always on the wrong or unintended surface. If it does not rotate, like in an extension cylinder application, using retention methods that prevent translation (sliding) may suffice.
Examples of this are snap rings, cookies, or cross drilled holes. If the pin does rotate, effort will need to be made to force the pin to rotate on the bearings.
Examples of these are pins with welded flags, tuning fork retention plates and buckeyes (or banjos). My favorite is the weld on flag plate. If the bolt holding the tuning fork or buckeye falls out, it may be lost leading to unintended pin movement and down time to replace.
Contrary, a flagged pin would be retained. The buckeye can also be subject break in cases with large, highly load articulations. Because of this, I have converted most legacy buckeye designs to a welded flag design.
In all cases strive to have double retention in each pin. Double retention requires two things to fail before the pin can be removed.
Assembly
The final thing to consider is assembly and disassembly. Be sure to start with the pin design. If using a flagged pin, I recommend turning down a step in the bar stock part of the pin for the flag plate to slip over. This accomplishes an easy way for the welder to locate the flag plate.
Second, this makes a stronger joint requiring the weld to be pulled through the plate in order to fail. Looking at the leading edge is also important. We can all realize that a sharp edge on the edge of a pin doesn’t allow for easy assembly. Most pin designs utilize a small 45° chamfer at the end.
These are easy to manufacturer and relatively easy to install. It also allows for a shorter overall length. Where possible, I recommend a 30° chamfer with a fillet on each edge. Modern CNC lathes make this complex shape easy to manufacture.
When used with fiber backed bearings, this leading edge will prevent tear out in the event of misalignment at install.
If the overall length doesn’t allow for the longer chamfer, try using a “bullet”. Named for its shape, a bullet is a temporary tool used to insert the pin and then removed. The bullet will have the 30° chamfer (or less) with fillets and simply bolts into the holes used to mount the cookie retention plate.
The final thing to consider in assembly is to consider how the parts will be pinned in reality. Is there enough room to insert the pin? Do I need to cut a hole to allow for a driver bar? Is there enough room to swing a hammer without contacting expensive or easily breakable items? Is there access to cranes or other lifting equipment so that this can be assembled safely?
Complete the thought process for disassembly. Can I remove the pin easily? Can I attach a slide hammer to ease disassembly?
Conclusion
My go to choice for a pivot pin is Turned Ground and Polished (TGP) Pre-Chromed Stressproof (ASTM A311 Class B). It has 100 ksi yield strength, good ductility, weldable and can be hardened to about 130 ksi. This will have a a welded lug for rotation lock on one end and a snap ring groove on the other.
As you can see, there is a lot that goes into pin design and we didn’t even talk about loadings! The goal of this article is to allow you to confidently design a pin that will give many years of reliable use…the first time. Good luck in your design.
Easily Learn the MathCAD Basics in 10 Minutes (Part 2)
As a followup to MathCAD (Part 1), Corey continues to provide an overview of MathCAD for use in engineering calculations.
