Calculating Torque Resistance of a Split Ring Collar on a Shaft

[daneran]

Hi.
I'm a student and working on a project I have designed in Inventor. For this project I will use a split ring collar. The m6 screw (not shown) tension is 17kN.
How do I calculate how much torque this ring can resist when clamped on a shaft?
Dimensions are ID 30mm OD 50mm width 30mm

Dan

 

[Nidum]

Finding the torque resistance of a collar with this type of clamping arrangement analytically is very difficult indeed .

You may find it much easier to either use a collet lock collar or a solid collar with splines or a keyway to take the drive .

 

[daneran]

Is there not any way to calculate it that is simple and not that accurate?

 

[Nidum]

Proper answer is that no there isn't .

The calculation essentially requires working out what the contact stress distribution is between shaft and collar bore . Relatively easy for a simple press fit but near impossible for your arrangement .

If this is just for a paper project you could do a very simplistic calculation for breakaway torque assuming that when the screw is sufficiently tensioned the collar effectively becomes a solid ring with a bore which is an interference fit on the shaft and then use the standard calculation for torque carried by press fits .

Not very accurate and more than a bit unsound technically but possibly adequate for your purpose .

 

[JRMichler]

What you call a split ring is what I call a clamp collar. I have used them many times where I need strong holding force or torque. They work especially well in applications with reversing torque, where a key would hammer loose.

A thick ring with a single screw, such as shown in your figure, must be a snug fit when you slide it on the shaft. If it goes on loose, the screw force is used up bending the ring around the shaft.

The analysis procedure is easier to understand if you start with a two piece clamp collar. Here is an example: https://www.mcmaster.com/#6436k18/=19n4anv. Imagine that the two ring halves flex enough to mold to the shaft. Then you adapt the equation for a thin wall pressure vessel: 2 * Fscrew = 2 * r * P, where
Fscrew = force from screw
r = radius of shaft
P = pressure between clamp collar and shaft

This simplifies to P = Fscrew / r.

Then the total contact force between the clamp collar (total for both pieces) is: Fcontact = Fscrew / r * 2 * r * pi = Fscrew * 2 * pi, where
Fcontact = total contact force (not pressure) between the clamp collar and shaft

Then the slip force is the contact force times friction coefficient: Fslip = Fcontact * mu, where
Fslip is the force to slide the clamp collar on the shaft.

The slip torque is then Fslip times the shaft radius.

The total contact force is exactly the same for your single piece clamp collar with one screw because tensile stress in the collar opposite the single screw provides the same tension as would a second screw.

The analysis gets tricky if the collar is thick and fits loose. In that case, part of the screw force is used to bend the collar to fit the shaft. That part of the screw force that bends the collar is not used for clamping.

 

[daneran]

Thanks a ton for that reply!

This is what I did..
Fcontact = Fscrew * 2 * pi= 17kN * 2 * pi = 106.76kN
Fslip = Fcontact * mu = 106.76kN * 0.8 = 85.4kN
T = Fslip * r = 85400N * 0.015m = 1281Nm

Thats a lot of torque. Way more than I thought I would get.
Did I do something wrong?
Assumed 0.8 mu for friction between steel and steel.

I am aware that a close fit is necessary so that the force doesn't get eaten up trying to compress the ring..
I was thinking to turn the ring ID to 30.01-30.05mm.
https://www.physicsforums.com/file:///C:/Users/DEA/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png

 

[JRMichler]

Your answer sounds about right. That's why I like clamp fits - they hold really well.

Whenever I design for "not slipping" steel on steel, I use 0.25 for friction coefficient. It's usually somewhat conservative.

Be aware that you need to torque the screw to its rated torque to get the rated clamp force. With socket head capscrews, that usually requires a cheater pipe on a good quality Allen wrench. A torque wrench is highly recommended.

 

[daneran]

Ok, I will use that friction coefficient aswell.

I did make an excel sheet for this project to calculate how much force I can get out of a 12.9 bolt with a limited thread length in the clamp. Interesting stuff to learn. Used the motosh equation for calculating torque on the bolt. The clamp is made out of a much softer and weaker material - S355 mild steel, so I needed to make sure that I did not strip the threads.

Do you have some litterature or referance for the calculations you showed me? I'm interested in learning more.

Could you help on this friction calculation aswell?
Two M5 12.9 bolts each with a preload of 12kN.
They are clamping a disc brake rotor to the clamp collar.
I need to figure out how much torque it takes to rotate the disc brake rotor on the clamp collar.
The bolts will stop movement in shear, but that's not what I'm after. The disc brake is used for a positional lock so it must hold on friction alone.
Clamp collar ID= 30mm OD=50mm. The distance between bolts is 38mm.

 

[JRMichler]

I don't recall seeing these calculations published. I needed to calculate a clamp fit one day, and realized that a half circle clamp (two bolts on opposite sides) had a free body diagram that looked exactly like that of a thin wall pressure vessel. If, that is, the clamp was thin enough to conform to the shaft. The second realization was that a single bolt clamp had exactly the same free body diagram if I sawed it in half opposite the bolt. It did not matter if there was a second bolt, a hinge, or a continuous piece of material.

Analyzing the disk attachment is similar.
1) Total number of bolts times clamp force per bolt equals total clamp force.
2) Total clamp force times friction coefficient equals slip force.
3) Slip force times radius = slip torque. Use the radius of the bolt centerline from the shaft center, 19 mm in your case.

Be aware that the shaft collar moves when you tighten its clamp bolt. The disk attachment bolts should be tightened after the shaft collar clamp bolt is tightened.

 

[daneran]

Alright. Thanks :)

For reference I found in chegg solutions for shigleys, Chapter 5 problem 67 is a split ring collar clamp. It's calculated the same way you have shown here.

 

[JRMichler]

For reference I found in chegg solutions for shigleys, Chapter 5 problem 67 is a split ring collar clamp.

Good engineers cross check...

 

[Rx7man]

Those split ring collars are usually not used for clamps on a rotating object.. they're usually used as stroke limiters on air cylinder, positioning of something on a shaft, etc where the force is along the axis of the rod. Anything holding a brake, etc I would VERY highly recommend a keyed or splined shaft!

 

[JRMichler]

Shaft keys work very well with unidirectional loads, such as a motor driving an entire machine. For reversing loads, they do not.

Much of my experience is with high speed paper converting and packaging machines. These machines use large numbers of servomotors. Many of these servomotors are running high rate acceleration / deceleration motion profiles. These applications use clamp or shrink fits. Here's a (randomly selected) example of a gear reducer designed for these types of applications: https://www.stober.com/input_for_SERVO_motors/. Click on Motor Mounting Instructions for MT, then read the first two paragraphs.

Another example is US Patent 6,832,886. You can look it up at patft.uspto.gov. The separator finger assembly in Figure 4 (and following figures) weighs about 45 lbs and makes a 9 inch horizontal move in as little as 150 milliseconds. It does this 24/7 for years at a time. The drive sheave is attached to the drive motor with a shrink fit.

Patent 9,604,381 has a belt / brush mechanism (not shown) that goes through an accelerate / decelerate cycle up to four times per second. The belt drive uses a clamp fit.

Keys are nice where you need to align something at assembly. Reversing loads need to clamped tight enough that the key does not carry the load. If the key carries the load, a reversing load will fret and wear until the entire connection is worn sloppy loose. So these applications use shrink or clamp fits. Shaft collars are just another clamp fit, where we adapt a low cost commercially available part to do a job. Some shaft collars are drilled and tapped as the OP wants to do. Others have something welded on.

IMPORTANT: Keys only need engineering calculations in highly loaded situations, while almost all clamp fits need to be calculated.

Shaft collars were originally designed for use as linear travel stops. That does not limit them to only those uses.

 

[Rx7man]

How about a taper? Perhaps a browning bushing?