Transmittable torque with an expanding mandrel 1

[joshdad]

Can someone help me please.
I am trying to calculate the trasmittable torque (expanding force) from an expanding mandrel.
The design is essentially a 24 degree (12 a side)cone being pulled toward a fixed blate by a 2mm pitch M16 bolt.
The expanding mandrel has 8 jaws that slide up the cone axially and expand radially. The bolt has a torqued of 20Nm.
If you are able to help I have a sketch that I can post (dont know how to attach it to this). I would also like to know the effect of using different pitch bolts (same torque)and also changing the cone angle.

 

[GregLocock]

Pity you fell asleep in that lecture, eh?

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[joshdad]

Wow sarcasm.

Asked for help and got that. I knew this site would be helpful.

 

[handleman]

This doesn't sound like a problem that's too difficult to analyze a piece at a time. However, it does sound like you have a lot of frictional factors between your input (bolt torque) and output (mandrel force) that may be tough to factor in. Break it up into 2 steps. I'm sure there are loads of places on the web where you can find bolt tension related to torque. After that it's an inclined plane problem.

 

[joshdad]

I have tried inclined planes to resolve this.
The problem I have is that I am also using inclined planes to determine the pullexcerted on the cone by the screw thread. When I factor in friction (because the angle is so small) I am getting wildly different results for small changes in friction.

I am looking for a more direct formula or someone to validate my formula.

I did stay awake during the lecture. The problem, as always, is relating abstract theory to the bits of metal in your hand.

 

[zcp]

Can you rig up a test setup where you can measure the force (either at the bolt or due to expansion) versus several torques? This will allow you to quantify your friction factors so you can ask your latter questions.

Handleman is on..... 2 step problem. But your test may quantify the 'slack' in the system.

ZCP

http://www.phoenix-engineer.com

 

[handleman]

It seems to me as though you're dealing with a statically indeterminate system. You can figure the frictionless mechanical advantage of the system relatively easily, but adding friction from the bolt-cone, cone-mandrel, (and mandrel-workpiece?) interfaces may be next to impossible. I concur with ZCP in suggesting that an experimental method is probably your best hope of getting meaningful numbers.

 

[joshdad]

Experemental is not an option. This is a one off unit
Can someone give me the formula for a frictionless setup. I have a formula based on the combination of an inclined plane replacing the thread and the cone but would welcome someone elses ideas.

My biggest worry is the losses due to friction. Looking on the internet is validating my calcs for friction losses.

 

[diamondjim]

If your torque is fixed at 20Nm,
it seems to me that defines the
pressure and preload of interfaces.

 

[GregLocock]

You have two separate issues.

What is the axial tension in the bolt, for a given torque? It will drop as friction coefficient (say 0.147) increases.

What is the torque capacity of the cone for a given axial preload? It will increase as the friction coeffcient (say 0.3) increases.

For a given geometry in each case the answer will strongly depend on the assumed coefficient of friction.

The interaction of the two friction coefficients will not be straightforward.




Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[zcp]

For the sake of continuing this discussion and since I only have a few minutes to look at this today, I thought I would post some additional information sent to me by joshdad which I will post a portion of here (hopefully that is okay, joshdad)

---- from joshdad------
My history regarding this project is very short. I work for a company who produce tooling. I am a fairly recent addition to the company (4 months). My history is in machine design with a brief time designing jig and fixtures.

The mandrel is round. The clamping diameter is 105mm.

I am trying to use the basic idea of inclined planes to determine the magnification of forces. The screw thread I have treated as a ramp. A M16 bolt has a dia of 50mm and at a 2mm pitch. My angle for the ramp is 2.3 degrees. ..[calcs].......................This force is the pull on the cone which has an angle of 12 degrees per side. ...............[calcs]............

But I know I will have friction losses. And I also think that I need to relate the transmittable torque to the outside diameter of the jaws. If my basic understanding is OK I am willing to impose a standard steel / steel friction on both the bolt and cone but do not know how to relate the friction. Is this dependent on how much thread is in the nut or is it a constant. As the actuating item is a cone I have line contact only, do I need to consider friction for this, as the contact area is very small.

I have questions but no answers. Even when the unit is manufactured it would be difficult to isolate the different factors and just blindly measuring input to output just answers this one specific design whereas I would like to know the formulas to apply to other designs.

--------------

ZCP

http://www.phoenix-engineer.com

 

[zcp]

Now I'll post my response I was going to send to joshdad, but decided to post here to keep the thread going and to show just how bad I am at trig while in a hurry (someone check me, please).

I am assuming that the mandrel is threaded so that when the bolt is turned, the mandrel moves in a straight line (doesn't turn). If that is the case and assuming your bolt has a washer face on the head side, you could use an equation relating torque to preload (force) in the bolt and thus the force pulling the mandrel in contact with the jaws.

T = K*Fi*d

T = torque (in your case, 20 Nm)
d = bolt major diameter (16mm or .016m)
K = torque factor that takes into account the friction in the threads and at the washer face
K = .3 for nonplated, black finish
K = .2 for zinc plate
K = .18 lubricated
Note K is based on experimentation, is not completely exact, but according to the tests, will get you close

So let's solve for the preload
Fi = T / K*d (assume plated K=.2)
Fi = 6250 N

Note that force is in N, not Nm. Torque or moment is in Nm (or force times distance).

Now let's transmit our mandrel force onto the jaws...
If I assume only one jaw and work through the trig, I get
Fjaw1 = cos2(theta)*Fi (that's cos squared)

If we have eight jaws,
Fjaw = cos2(theta)*Fi/8

For your case, I get
Fjaw = cos2 (12deg)*6250 / 8
Fjaw = 747 N at each jaw


Now if your mandrel is spinning, you have a clutch disc problem and have to account for that.

Hopefully someone will take it from here.


ZCP

http://www.phoenix-engineer.com

 

[joshdad]

Before anyone gets there before me.
"A M16 bolt has a dia of 50mm and at a 2mm pitch."

I know its wrong. What I meant to type is a circumference of 50mm.

 

[GregLocock]

zcp, your bolt force equation ignores pitch. I'm not saying it is wrong in practice, but that is rather a surprising outcome.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.