Help Needed with Material Stress

Tip of a fishing rod?

Fiberglass is a consideration, but it would seem CF would be even more resilient.

McMaster-Carr sells both as well as 304 stainless, but I feel 304 may not be much better.

Chamfer the hole and lay a bead of semi-rigid epoxy around the wire to act as a strain relief.

Or machine a chunk of nylon to act as a ferrule, like they use on graphite golf club shafts where they meet the club head.

Good thought. The question is if the ferrule would deform over time. I think epoxy would.

I don't have a solution, just questions.

Which are the "must keep" dimensions, 0.972", 5 lbs and/or 12.5 degrees? Must it be a straight wire or can it be coiled or wavy?

The must keep dimensions are .972", 5 lbs ±15%, and 12.5° ±1°.

The current view in my rendering is from the side, but the wire must move in both the X and Y direction (as looking down from the top).

There is some room to coil the wire. The base slides into a cavity that is .62" in diameter.

I've looked at it more closely and of course there are some practical difficulties in actually tapering it as the diameter is so small (but it's surprising what you can acheive with a few stroke s of a needle file).
If you maximise the length of the sping limb, by removing the top section of the support block, that would give about 20% extra spring length!
Make the wire say taper from say 3/32 to 3/64 it should be much better. Of course a less rigid material would allow slightly bigger dimensions, nylon rod? Or molded plastic?
De
(Please send Tuna immediately)

The top part is where strain gauges are attached to measure the force applied to the top of the wire.

Tapering is an option. The wire would need to be ground to the correct diameters and then heated and quenched to the desired hardness. Seems like more possibilities for variation in the process and thus a lower yield.

The top part is where strain gauges are attached to measure the force applied to the top of the wire.
I don't understand, the mounting block surely doesn't have any stress on it? it's solid and solidy fitted into a socket.
I thought you said the spring is just a return spring?

Del

Yes. The top section that captures the rod will receive strain from the bending moment of the wire. That top rectangle that encapsulates the wire holds four strain gauges.

Think of it (the base) as a larger diameter rod with a thinner rod sticking up out of it. That thinner rod is just a flexible lever sticking out of the thicker rod and while the thin rod bends due to the strain force, so too will the lower and thicker rod, but only a tin bit.

Since the mechanical deflection of the base is not perceived by the user, we add a flexible wire to give the user feedback as to how much force they are applying to the control.

Ok, I geddit (nice explanation btw).
Ok how's about a bit of lateral thinking and copletely reverse the design.
Have a long relatively rigid rod with the strain gauges on, and have it stuck into a block of rubber which replaces tha top section of the mounting block?
Seems like a rubbery idea to me.
Del

Good thought. That would work, but requires a lot more redesign. Is there a simpler method?

The simplest would be replacing the existing steel rod with a rod of another material that is more robust. That may not be possible, but it is my first stab at the problem and would represent the least impact on the design.

Use an alloy with high yield strength and low Young modulus a beryllium cooper, or may be some titanium wire (I do not know if available). As you explain is it thumb joystick ? Are you obliged for ergonomical reasons to increase the stroke ? I designed such joysticks but the the stiffness was not unaccepted by users. I shall check tomorrow if from the strength point of view your design is valid. How many operation till it fails in actual configuration ?

I was thinking of BeCu but hadn't had a chance to check it out. For some reason Ti seems too brittle to me.

Stroke and force are as per customer requirements. We can give or take a little if required.

I don't have a MTBF to give you.

Is there a simpler method?
Yeah, taper the d*mn rod... it won't give a lower yield than 100% breakages
Del

Copy tapering.

The harder you go the more sensitive to notch failure (aka, point stress)

I'd be inclined to use a thicker wire of lesser hardness - like oil tempered ASTM - A229

I'd also probably reduce the boss height by half.

I'd also put a slight taper in the top 1/3rd of the resultant hole. If you can 'bell' the taper profile - even better. However it will mean the spring rate will increase more rapidly toward maximum deflection, as the point of stress migrates up the bell, 'shortening the working wire length'.

Imagine a circle of radius ~0.25 tangent to the left edge of the rod where the rod enters the socket. Extend the socket according to the contour of a 12.5° arc of this circle. The rod will then bend along this smooth arc, rather than having a stress riser.

The radius may need to be adjusted to keep the bending always elastic. A straight taper won't help as much.

I was trying to think of a way to describe this "falling away" taper.

Thanks for that. It's rather small in diameter, but should be a piece of cake for a machine center. Or stereo lithography?

Anybodies guess - but if it was anyone who actually counted - they'd say so. Dead easy to do it anonymously - takes a bit more introspection, deliberation and courage to OT and ID yourself.

I shall put this 'on' and hopefully really annoy them.

Maybe "trumpet"?

Ok, same concept, thanks. I shall add that to my multilingual arsenal

Just out of interest Nick;

If you did what I suggested which is utilizing the entire depth of the mounting block and halving the height, and by way of 'bell' / 'trumpet' enabling the increasing l from 24.688 to ~32 mm, would it be within the properties envelope of the wire I suggested?

All ideas coming from an other are out of interest, I am accustomed. I wanted only to add some thing I did not mention since dealing with sensors you may know the fatigue limit in bending is under 1 E-3 (fatigue stress limit less 0.45..0.55 ultimate stress). In fact what was said corresponds to what I stressed the actual design is out of range. The increase 24.689 to 32 mm leads to a ratio 1.1 E-2 which although reduced is still too high. One should not forget that in this application there are 2 limits to be respected: yield and fatigue. Most probably the highest number of cycles will be for the range half so that one can say : for the whole stroke the stress should be less 0.7..0.8 of the yield strength and for half stroke less 0.8 from the fatigue limit in bending. Please check if this corresponds to the recommended wire if this is the case accept the 34.5 solution. I am only asking myself how you could transmit the torque to the measuring zone.

Fair enough, as d will rise to obtain the poundage, might be chasing one's tail, though I felt 0.2" deflection in 1.3", would have been ok.

So what is really required is a rethink on how to do it;

Of course the above also applies to the taper idea, which also leads to greater tip inclination at the gauge attachment point, (if that matters?)

The intermediate coil idea, solves the stress aspect, but presents a leg alignment/concentric concern in production.(if that matters?)

Ummm ...

So what do you think of boring out & tapping the boss, to take a rigid 'stick', headed with a disc, which is held down by a conical compression spring, seated against a threaded ring in said threaded bore?

That ring/spring then sets/adjusts, the poundage to tilt the stick.

Probably make the gauge attachment easier too?

Thanks for the analysis.

If I read this correctly, then even carbon fiber (CF) will fall short of the requirement because the ultimate yield strength for CF is only 2 to 3 times that of music wire steel.

Another approach is required.

Spoke from some kind of bike?

Although these problems are solvable analytically, I prefer to use imagination to provide the proper direction, and then math to optimize the solution. In this case, one needs to increase the diameter of the wire at the base to lower the peak stress and eliminate the breakage. This will also make the wire stiffer. Then one must taper the wire until one achieves the desired force/deflection response. If you don't need the same response in all directions you might consider making the cross section a rectangle instead of a circle. However, the same principles apply. Music wire is a good choice because of its high yield strength and elastic modulus. However with proper design, many materials can satisfy your boundary conditions.

Ditto on chamfering the hole. If your drawing means that there is a sharp corner on the hole where the rod is mounted, it's a stress raiser. Chamfer the hole, round off any other sharp edges.

My recommendation would be to use a Nitinol wire. The combination of the nickel and titanium give the wire unique strength and memory characteristics unmatched by other materials.

The main problem seems to be that the hand has no idea what 12.5 deg. looks like. If you are actuating strain gauges, you could try a thicker rod. If 1/16" Dia. is critical maybe an appropriately sized collar can limit the travel.

Does the piano wire meet the rest of the requirements?

Obviously this solution will be unacceptable in most circumstances, but: can you just make it easy to replace and accept that it's going to break periodically.

Ha! Maybe if you taper the mounting block where the strain gauges fit and allow it to flex a whisker more you will be killing several birds with one stone, you'll effectively be increasing the length of the beam, you'll be spreading the load at the mounting point and you'll probably get a bigger signal from the strain gauges. The mouning block is presumably machined and thus tapering it will be easier than tapering the rod.
That's a win win win win in my book.
Del

I concur (see Catch Me if you Can).

Even a small radius at the top of the boss hole can make a huge difference in point stress distribution and resistance to fatigue.

Given that small radius, then a 1/16 CF pultrusion (or slightly smaller) would be worth trying, I'd think. (I have dealt with Avia Composites, but they have been bought, so I don't know how much DNA remains.)

• **Diversified Composites, Inc., Erlanger, KY: Announced the acquisition of Avia Composites of Hickory, NC which specializes in the pultrusion of carbon fiber for aircraft, industrial and sporting goods applications. Avia developed an "active surface chemistry" to enhance bonding between pultruded carbon fiber profiles and prepreg materials. Reggie Durham and Sean Reymond from Avia have joined Diversified, as has Mike Yeats, formerly with Pultrone...

A spring steel coil with the axis of the coil vertical, and the coils not touching (and with thicker wire to get the spring rate back) would also probably work. Most of the deflection would then show up as torsion in the wire, spread over a long distance. (Think base of some vehicular communication antennas.)

Custom spring makers have good magic that allows them to very quickly (even over the phone in my experience) say how long a spring will last under a particular usage. Diamond Wire in Pittsburgh is one that I have used.

I would suspect that your fatigue is being caused by the sharp corners at the "point of greatest stress". Perhaps you could try machining a round champfer at this point.

You might look at mobile antennas which are designed to be mounted on vehicles. I don't know if there are any at the dimension you need but I know mine take a heck of a beating over time when I hit tree branches etc.

Using your present configuration the peak stress at the base of the rod is about 198ksi. This is the maximum stress will be and it is marginally high, even for music wire. If you were to increase the diameter at the base of the cantilever from 1/16" to 3/32" the stress would drop to 68ksi. This is within the elastic limit of many materials. The bad news is that your deflection will be too small with a diameter of 3/32". This is why you want to taper the control rod. By proper tapering, you can achieve all your objectives.

Thanks, I just need to work out the details, but tapering is simple (relatively) to do.

So the easiest thing to try is to move the stress point farther down the rod, to let more of the rod flex. This might also accomodate a larger rod to maintain the desired pressure on the doohicky.

Maybe fit it in a spring?

Can you telescope? Like keep some winding on a sufficiently sized nickel cored bass string and use that end to compensate for stresses at the lower end.

What is the frequency of the back and forth?

Is it in an hot environment?

Considering the dimensions 5 lb's is a lot of force to bend the wire. What does it do? Is that the force it takes to get it out of neutral?

Hope it works out, Ky.

My bad, never read the whole thread. At least I got the taper bit right, somehow.

ky -- yours is the best solution so far.

And 5 lbs +/_ --%,12.5degree +/- --% does not match with Steel E .

If X &Y co-ordinates are the only directions of displacement - 4 flat springs say 2mmx0.5 mm placed 1 mm away from this CRITICAL 1/16" Spring --- to 10mm up-- will behave like automotive HELPER Springs-- and stop all fatigue cracks

mm

If you ask I can send 4 pcs of High-Strength Bamboo strips to act as helper springs .

Your Postal address will be needed.

A couple of comments. First, all the math you need to create your control stick is available from texts such as "Formulas For Stress and Strain" by Roark and Young. A tapered beam would provide a nice solution. A constant stress column would be a 3rd order exponential horn. A linear taper could also be made to work. And, if it's any easier, a stepped column with two or three diameters could also do the job. It depends on detailed requirements and resources. A neat advantage to the exponential horn is that if you use strain gauges, the length and location of the gauges is less critical.

The second comment is that your present design (assuming that the dimensions are in inches) won't come close to providing the performance you require (even if it doesn't break). The deflection of the 1/16" music wire will be about 1/16" at 0.972 with a 5 lb load. If you exceed the 5 lb. load force, the rod will break.

welderman, I'm so glad you wrote that, I thought we were dealing with a real problem but I couldn't make the deflection work, I was getting a permanent set in the wire.

The stress is inversely proportional to the diameter, so the constant stress solution would be shaped like an old fashioned peg leg, ending with a point at the point of load.

A thinner wire would have the flexibility, but not the resistance to load.

Perhaps a thicker wire with a short coiled section in the middle would work. thicker to reduce the stress and the coil to add enough flexibility.

BTW, the belling of the opening in the mounting makes no difference, the wire is not in contact with the curve, it is still a sudden loss of contact.

Oops. "The stress is inversely proportional to the diameter," should read, "The stress is inversely proportional to the diameter cubed,"

A little more research and I found that this material is in the region of ten timed stronger than I thought. I still agree with welderman that the deflection under the five lb load is only about 0.06".

ASTM A228 material.

I just left 1" of a 1/16 drill bit (only the smooth partwas exposed) projecting from a 1/16 hole. It took about 2.5 lb to deflect the end 1/16". At 5 lb, I was wondering if my drill bit would survive (at about 1/8" deflection). The bit would not have survived a .216 deflection.

So, I think your numbers are pretty close.

I admire your lack of trust in the computing of bending moments stresses and the rest.

"BTW, the belling of the opening in the mounting makes no difference, the wire is not in contact with the curve, it is still a sudden loss of contact."

The principle behind the belling is to make the working wire longer. So unless you have belled almost to the bottom of the boss, there is insufficient working length for the defection required. Additionally, the bell curve must be precise if you expect to achieve the desired end load out of this diameter wire/material.

It's analogous to putting a leaf spring with same load capacity, but half the length, on a cars suspension, then expecting the same range of movement not to exceed the properties. But having done so, and perhaps discovering it can't be made longer, what do you do to get sufficient 'working material' length per unit deflection?

Surely, just reducing the the height of the boss would be sufficient! If you intend that the bell interfere with the shape of the bent wire, that would reduce the desired effect, not help, and might have to be individually adjusted for small differences in the wires.

With the memory of calculating expansion loops in piping, I still think the answer is likely to be found by coiling the wire in the middle of it's height, gaining length, albeit, acting in torsion, but it seems the most hopeful to me. I confess that I don't know how to calculate the effect though.

That's true in principle, as you are increasing the working length by coiling, so stress per unit length falls. But as said, it is difficult to get the two tails aligned in manufacture.

You would also need a bigger wire diameter. But if you read Nicks post #29? the math to find a diameter and length is there for the using.

The bell is just a way of having it stiffen up and migrating the stress point. Pick the right diameter and length for the deflection and load - redesign the 'holder' to accommodate that wire and 'problem solved' - no bell required.

Will it fit - can the holder change - what is it made of (in terms of anchor stress / depth) - what are the actual holder dimensions - is there space underneath - who knows

And I guess that lack of 'engagement' in solving is why ICBA to pick up a book, or calculator, or try plugging in something like 3/32 piano wire around 1½" working length into Nicks math.

Very surprised that you send to my comment you wrote it is "just out of interest ".

Did you change your point of view ? Is it now a good answer ? Or does it stay further as a out of interest answer ? I would like to understand.

"Just out of interest" is a casual conversational device known as a 'leading statement'.

In this case I'm recognizing the veracity of your failure analysis - but seeing you stopped at 'it will always break' - I thought if I threw you an alternate 'sample' I could 'lead you' to going the extra step and perhaps demonstrate 'working it backwards' to obtain a wire solution - as I logically divine you can do this for AH.

Did I change my point of view? no

I was/am, quite content to just point people at the solving path. To my mind that is more productive than a vote.

But as it seems you'd like one - and 100's of less worthy contributions seem to get them - have one on me.

When ever I feel stress I take a few deep breaths

NO ^10 = NO*NO*NO*.......*NO ten times! To use your notation: d= F*L^3/(3*E*J) where F is the applied LOAD in your suggested equation LOAD does not appear. Please try to make a dimensional analysis according to your suggestion d(which is a "LENGTH") has the dimension L^3/( F/L^2*L^4) = 1/(F*L). This also shows that your equation is wrong. Several sources can be used if you do not believe what I wrote among them the ROARK book is a very good one ( In Roark veritas !).

It must have been too late at night when I wrote that. Leaving out F was the worst; the other mistake was with which numbers go with which support conditions. Thanks for catching!

You are close, but the equation must include the force that causes the deflection.

Using your terminology, it is d=FL³/3EI where F is the force in pounds.

Sorry AH, but it comes down to finding some magical material to replace the music wire.

Calculations show that the wire only deflects about 1/16" under a 5lb load at a 0.972" moment arm.

Lengthening the arm will increase flexibility but also increase the bending moment and, the already too high, bending stress. The stress in the example is in the region of 203,000psi, higher than the normally recommended 45% of the range 230kpsi to 399kpsi. I think the 45% does not allow for the number of reversals envisaged in this case.

Unfortunately, any increase in diameter to reduce the bending stress has an even greater stiffening effect on the wire.

Congratulations!! You just demonstrated that you clearly understand the principles involved. You will now understand why a 3rd order exponential taper will provide a beam with constant stress along its entire length and give the maximum deflection permitted from a steel rod. If that's not enough, you need a lower modulus material such as BeCu or Ti. For OP, you need not anneal the steel rod to grind the taper. The grinding is best done in the full hard condition. Just remember the ball bearing motto. "First you make them hard,-then you make them round".

I saw need for a curved taper a few posts back but consider; If the 1/16" wire is radically overstressed by a factor, perhaps, of four or five, the tapered wire would have to be greater than 1/16" at the halfway point or it would be seriously overstressed there. In fact, 1/16' might be about right at the quarter span point nearest the load. Good bye flexibility.

Actually, I'm of the old school that doesn't think in terms of "a 3rd order exponential taper", we used methods of successive approximations, moment distribution and the like. I could probably figure out the equation for the wire to be automatically shaped.

It shouldn't make any difference how old your school is (mine is likely older than yours). And it shouldn't matter whether you calculate the exact equation for the taper, or design it by successive approximation. When the taper is correct, the bending stress along the entire length will be constant. This form provides the maximum deflection without over-stress. So, if you design for 20% less than the yield strength or whatever safety factor you feel appropriate, (say 150ksi for music wire), and you design the taper correctly, the stress anywhere along the wire length will be 150ksi. By the way, lower modulus materials will provide greater deflection, but I would stay away from composites. Their properties are not isotropic and can cause problems with strain gauges.

I am using 1/16" music wire purchased from McMaster or MSC. I just placed the part into the test jig again and measured full deflection of 12° at just over 5 pounds force using a calibrated digital force gauge.

I don't doubt your equations, but empirical evidence seems to indicate that the material I am using probably has a different modulus than what you are using.

Hmmm. That suggests a modulus of 9,500,000 or so. Most steels are very close to 30,000,000. Are you sure that the wire is really 1/16?

Is the 12 degrees actually measured as shown (.216 deflection at .972 up).

It occurs to be that 16 gauge is .0508". Could it be 16 gauge, instead of 1/16 inch? That would produce essentially the deflection force you provided.

I pulled one out of stock and it is 0.0625"

I think you're right.

If we reduce the wire to 3/64" the deflection at 5 lb is .215" -- as if by magic. But the bending stress at the base is way, way to high: 481 kpsi.

Various carbon fibers don't seem to offer the right combination, either, (although HS2 fibers, which are high strength but medium modulus are a little better than steel). A 3/64 pultrusion would give about the right deflection and enough strength (if the 725 kpsi is retained in the pultrusion) to work a few times.

So tapering is a possibility, as is mounting a larger diameter rod in an elastomeric.

Cheapest alternative might be to use 3/32 wire, and put three or four spaced coils near the base, ala an antenna mount. A good spring winder could knock these out with high repeatability and good concentricity between the upper and lower parts of the wire. Stress at base would be 60 kpsi or so, and the force could be easily changed by changing the number of turns and their diameter. With a piece of copper clad steel welding rod, one could mock one up in a couple minutes.

Maybe something like this?

#48

This thing should make a nice sound too

I was thinking more like this, with the wire extended in the direction of W to form the joystick end. (Shown upside down, because I am lazy.)

Yes, that makes an interesting solution.