To translate axial F to tensile force of screw 2

[aaron72]

Started a new thread to go deeper into the concept.
Like to find out how:
1) to determine if the SS M5 screw or the Al collar will break by translating the axial force hitting on the collar-shaft assembly. see attached picture. F acting on the collar is parallel to collar-shaft assembly.
2) likely where is the highest stress area?
3) Is radial force the right way to determine friction force? Friction Force = mu x Radial Force in this scenario?
4) or using Normal Force for collar inner circular surface area into F=mu x N.
5) how does the collar inner surface area will relate to the friction force between the collar and shaft?

advice/input/guidance will be much appreciated!

thanks!

 

[desertfox]

Hi aaron72

I have uploaded a calculation of the loads on the collar and how to calculate the screw axial force from its torque.
This is highly theoretical because I am assuming the resultant loads on the shaft are from a uniformly distributed load which in practice will not be the case.
Your best bet is to estimate the forces as I have done and then carryout some practical tests and measure the forces.
The formula for axial force from bolt torque again is only approximate and there are other formula which give more accurate results however I think for your situation this formula should suffice.
Info on bolt loading can be found here:-

http://www.roymech.co.uk/Useful_Tables/Screws/index_screws.htm

 

[aaron72]

Desertfox, thank you very much!
a bit rusty for me, on the 2P from bolt to cause 2x 2P at the max diameter area? any reference or link that I can dwell further?
yes, will prepare for actual test to get actual data. Thanks again for the suggestion!

 

[desertfox]

Hi aaron

I took moments about the bottom half of the clip, in the calc I gave dimension X and 2X however I guessed at the proportions of your clamp,does that help

desertfox

 

[Cockroach]

This is quite a tricky problem. The M5 stainless steel bolt is tightened to a prescribed torque, thus holding the Collar to the Shaft. What is that torque? That would give you the clamp pressure of the Collar to the Shaft.

Using a longitudinal force to shift the Collar along the shaft imparts a moment in addition to translation. Certainly friction comes into play as well as the surface finish between mating components. How far do you wish to carry the computation, theoretical wise?

You need to apply interference fit between the Collar and Shaft, therefore the bolt torque must somehow translate to radial friction. This may be tricky, I would guess that the bolt thread pitch shortening the circumference length of the Collar would directly be related to radial pressure. Yet the radial pressure is not uniform for the piece directly under the bolt does not count. So you have a lobed shaft. This will detract from reality and essentially introduce errors.

I think maybe an FEA would be a better tool.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[aaron72]

Hi desertfox
Thanks for the note. if the "clamp" or the "open ended collar" is a rigid one piece Al, without the theoretical pivot at the bottom, then the moment will not exist? or can use the shaft/center axis to calculate the moment?
Any suggestion how to determine the force acting on the shaft for friction force calculation.
attached a refine picture, hopefully you can clarify on the normal / radial force.
thanks!

 

[aaron72]

Hi Kenneth
Appreciate the input + thought behind.
Can shed some light on how the clamp pressure should be calculated if the torque on bolt is 1.5Nm, as posted in the jpg in reply to desertfox above. I still cannot link the surface area into the analysis.
Bolt torque to radial friction? T=0.2 x Fbolt x d? then F-friction = u x (2 x Fbolt)?
The collar is sitting (clamping) perpendicular to the shaft axis as it act as a mechanical stop to the parallel F hitting on the collar.
Next is trying to determine:
2) if the M5 bolt will break but need to find out how to translate the axial force to tensile force (perpendicular to collar axis) pulling the M5 bolt, or maybe the Al collar will deform instead of the tensile force acting on the bolt
3) if the collar will deform (bending along the Force parallel to the collar axis and shear)

sorry, was trying to follow the forum guideline, to split out the questions, therefore, started another new thread - as you have commented. BTW, this is not homework, it's a design analysis i am working on which i find it simple (design wise) but yet deep and tricky as you have mentioned - already spending time diggin the old mischke & shigley book

thanks!

 

[desertfox]

Hi aaron72

The way I see it is:- as you tighten the screw the bore in the clamp as to close in on the shaft and at the same time close the gap between the two faces which the M5 screw passes through, for that to happen there must be movement of the two halves of the collar towards each other no matter how thick the base is otherwise it won't clamp the shaft.
If you consider equal and opposite forces acting on each side of the clamp due to screw tension then clamp will close pivoting about the furthest point from the applied tension, which in this case would be the base of the hole which the shaft passes through.
I assumed that the resultant force would act at the centre of the shaft and because the resultant force acts at a distance closer to the pivot than the applied screw tension the force is magnified.
Again I stress that this is highly theoretical but I feel its a approximation whilst you do some practical tests.

desertfox

 

[Cockroach]

Aaron72....

I would use Interference Fits as per Thick Wall Pressure Vessel Theory. Noting the discussion to present, as you torque the clamp screw, I would initially assert the inner circumference shortens by the pitch of that screw times the number of revolutions tightening it. From that you can determine the diameter and then the interference on the Shaft.

Thick Wall Pressure Vessel equations will yield much of the information you need to know. Radial pressure and clamp holding torque would probably be what you are looking for. From the holding torque you can obtain the minimum force required to initiate motion impending. This is coupled to the static friction, 0.15 to 0.20 for steel-on-steel. I would suggest this is the force you are looking for.

UncleSyd has noted that the analysis should entail combined loads of bending moment and axial load. I believe this would be the last step, with the axial load offset from the centre line of the Shaft, you can set up at least one equation. I think it best that you add deformation to the matrix for the second equation, which would permit solving two equations in two unknowns, moment and axial force. Your previous analysis on axial force alone would be a measure of influence of that bending moment on the clamp.

Essentially this computation is similar to the old classic statics problem of a bolt & nut system inside the collar made of different material. As the bolt is tightened the reader is asked to compute the stress in the bolt shank and collar. Same-same in your case, except you have a circular clamp imparting squeeze to a shaft.

I find this a very cute little problem. I will work something through for you and post the PDF. This will be the mathematical model since you have not provided numerical details on shaft and collar, which doesn't necessarily matter. What is important is the analysis and approach to the problem.

So the rest of your questions, maximum stress through the bolt, the deformation of clamp and shaft, etc will bear out of the mathematics. Note that for shock loading, you need a different model, we are talking peek sustained static forces here. You would be interested in a collision and therefore elastic/inelastic transitions between contacting members during such an event.

As mentioned, not such a simple problem afterall. Let's break it down and go one step at a time.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[rb1957]

clamping pressure could be found from a free body of 1/2 the clamp ... loaded by the tube pressure, = a resultant acting thru the centre of the tube, and the M5 bolt tension.

but using mu*pressure will give you only part of the slip load, 'cause won't the collar rotate and dig in on one side, before slipping ?

 

[aaron72]

thank you Kenneth for the detailed input and looking forward to the proposed mathematical model.
thank you rb1957 for the suggestion! The collar will not rotate for it fixed to be in the current position, except it can shift along the axis when pushed. it should be a stop. Will check out the 1/2 clamp FBD.

 

[rb1957]

won't your force the clamp to pivot about (not along) the tube ?

if it can shift along the tube, i see it lifting on one side and diggin in on the other ... no?