Natural frequency of Shaft

[MetalGearMan]

Hi. I saw a similar thread with the same question. My situation is slightly different and would appreciate some advice. I have attached a schematic of the setup in question. The shaft in the middle has failed constantly and the schematic shows a modification that was done to reduce the stress on that shaft. The inital setup was where the motor and gear box was connected directly to the shaft without the use of the drive chain that you see. I have a feeling that it was failing due to excessive vibration that caused a fatigue in the shaft. Can someone who is knowledgeable in this area please advise me on how to calculate the natural frequency of the shaft and then compare it to the drive frequency of the motor?
The shaft was made of carbon steel AISI 1080 and the motor is running at 186 rpm at 7.5 HP.

Thanks

 

[GregLocock]

If those proportions are anything like accurate then I doubt you have a linear resonance problem.

Unfortunately the schematic is so sketchy I couldn't eve begin to work out the effective mass, but if it is roughly uniformly distributed across the shaft then you could make a stab at it.

Where did the shaft fail? at the bearing, or in the middle?

What did it look like?



Cheers

Greg Locock

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

 

[Kniplamp]

The question is indeed how the shaft did fail. This sounds to me like a torsional problem.

regards,

Jos

 

[Ron]

The shaft failure mechanism is being debated in the Mechanical Engineering Other Topics forum. Looks like a fatigue issue, but doesn't look torsional except the final failure. Looks like typical crack propagation until final failure.

 

[MetalGearMan]

Greg Locock and Ron

The shaft failed somwehere near the bearing on the right side. I have done some torsional analysis and it was not the cause of failure. The cause was due to faitgue or fast fracture. I need to understand what induced this fatigue, and whether the vibrational stress was the root cause.

Thanks

 

[BobM3]

Does "right" mean the bearing on the motor end? Did it fracture on the motor side of the bearing or on the other side of the bearing? From my other post, when the motor was connected directly to the shaft, you did use a flexible coupling to initially connect the motor to the shaft, correct?

 

[BobM3]

Do you have the ability to vary the speed of the motor? If so, slowly increase its speed and see if there is a speed at which the system gets loud or vibrates - that might be a resonant frequency. If you don't have a means to vary the speed then coast the motor down by removing the power to it. If it coasts down slow enough you might notice a speed where the system gets loud or vibrates.

 

[MetalGearMan]

BobM3

It fractured on the other side (not the motor side) of the bearing. Initially I dont believe it was a flexible coupling that was used. This might have made the system too rigid. Could this have lead to the fatigue? Is it still a vibration issue then?

I don't have the means to vary the speed but i can shut off the power like you said and try to determine where the vibration gets louder.

 

[Kniplamp]

The right side is the side where the motor mounted. Have you considered torsional resonance as a cause. I will show you an example of a shaft from a centrifuge, due to torsional overload.

 

[Kniplamp]

I am a bit confused here. The right side on the scetch is the motor side, yet you indicated that the fracture is at the non-driven end. If it is at the non driven end, torsion can not be the cause. In that case test the resonance, just do a bump test, take an FFT with an accelerometer on the shaft while hitting the shaft with a hammer.

 

[BobM3]

I think our browsers show the sketch differently. I believe the failure was near the bearing mounted near the motor. It occured on the side of that bearing opposite the motor.

It's possible that a rigid coupling (and misalignment between the original inline motor and load shaft) would increase the bearing loads which would increase the bending loads along the shaft. It's also possible that even with the shafts aligned, the increased stiffness made that end of the shaft more of a "fixed" end than a "simple support" end. Definately do the resonant tests anyways.

If you have weights and dimensions, someone in the forum could calculate an estimate of the natural frequency of your shaft.

 

[Ron]

If you look at the beach marks on the failure surface, they are multiple and close together, indicating higher cycle fatigue, not fast failure. When the crack propagation got the point of such a reduced cross-section, the torsional failure occurred (it twisted off what was left of the shaft after the crack progressed to about 2/3 of the cross section.

Do your torsional calcs with an area of about 1/4 to 1/3 of your shaft area and see what it shows.

As for the source of the problem, it is likely that the midspan of the shaft has an elliptical "orbit". This is likely causing a stress reversal in bending on the shaft with each revolution just prior to where it goes through the pillow block. Is this where your failure is occurring?

 

[JJPellin]

I think I disagree with your conclusion. On the face of it, the change from direct drive to chain drive should have increased the chances of a high cycle, bending fatigue failure. The chain is now a fixed side load on a rotating shaft. This causes a bending moment in the shaft that reverses with each rotation. You stated that the original direct drive arrangement was rigid. This throws up all sorts of red flags for me. I was always taught that you cannot put three rolling element bearings on a single shaft. It is impossible to perfectly align the three bearings. Any misalignment results in a bend in a rotating shaft, which is an ideal recipe for fatigue failure. You have never described the type of bearings. You never described the shaft location in terms of stress concentrations, keyways, steps, etc. Unfortunately, I also don't understand the machine this is driving. But allow me to theorize:

If the load from the machine was similar to an imbalance, it would rotate with the shaft and not produce a full reversal bending moment in the shaft. If the load from the machine is in a fixed direction and not rotating with the shaft, it could produce a full reversal bending moment. If the bearings are self-aligning (spherical bearings or a spherical mount within the housings) then the bearing would allow the bowed shaft to flex within the bearing. If the rigid mount of the motor on the outer side of the bearing prevented the bearing from flexing with the load, it could lock the bearing in place and the force from the fixed load would result in a high reverse bending moment adjacent to the bearing. Even with no fixed direction load from the machine, misalignment between the bearings in the motor and the pillow block bearings would produce the same affect. Changing to the chain drive removed both mechanisms, but introduced a new fixed load that could fatigue the shaft. But, apparently, this new load is not great enough to exceed the fatigue limit.

Vibration from the machine is unlikely to cause a shaft fracture. If it was a torsional vibration, it could break the shaft, but this was not a torsional failure. I didn’t notice any description of the vibration. A run-speed vibration indicative of imbalance should not fatigue the shaft. A two-times run-speed vibration indicative of misalignment could indicate a bending condition that might fatigue the shaft.

In the end, the answer is the same. Reduce reverse bending moments in the rotating shaft. Reduce stress concentrations at high stress areas of the shaft. Use a material with good fatigue properties, less brittle, not as notch-sensitive. It sounds like you accomplished a couple of these changes, but not all of them.

You did not do a very good job of describing the problem. You did not do a very good job of providing the available data about the machine design or vibration. Without much detail to go on, our answers tend to break down into speculation and result in frustration (as you saw on the other forum where you posted this same issue). Add double posting into the mix and you may not make many friends.


Johnny Pellin

 

[MetalGearMan]

JJPellin

I realise I did not do a good job of describing the situation very well. It is becaue I myself did not have all the required data and information. I have only seen the machine in opperation once and have had to make several assumptions in solving the problem. I myself have been frustrated in being given this project without the ncecessary tools to solve it. Therefore I fully understand everyone elses frustration in the matter. I do have a clearer understanding of the issues at hand now though. Thanks for your help and advice

MGM

 

[desertfox]

Hi Metalgearman

Looking at the file you uploaded in your post in mechanical engineering topics your fatigue failure started with the crack on the righthand side of the shaft and progressed across to the left as you look at the photo.
Now fatigue cracks only grow under tensile stresses, so the only two ways tensile stresses can be in the shaft are :-
Direct bending stresses due to external forces placed on the shaft between its supports and this should include loads applied to the shaft due to tensioning of the drive chain.
The other way is torsional stresses that generate tensile principle stresses which would occur at approximately 45 degrees to the axis of the shaft.
Using the site that "Allhandlestaken" posted in your previous thread I would say your failure was low stress cyclic bending.
I would start by analysing the bending loads on the shaft and calculating the maximum tensile stresses before I started looking at vibration and natural frequencies.
To this end I have uploaded a sketch explaining the torsional failure and how I would analyse your drive shaft.
I also have trouble understanding how the shaft stresses would be reduced by moving from a direct drive to a chain drive perhaps you could explain it to me.

regards

desertfox