# Radial Deflection of a rotating shaft

• billy_joule
In summary, the conversation involved a series of questions that became progressively more vague. The first question asked for the output speed and torque of a gearbox given the input power and efficiency. The second question asked for the design of a shaft to transmit the gearbox output torque. The third question asked for the maximum radial deflection of the centrifugal pump impeller at the end of the shaft. The conversation also discussed the use of sensible engineering assumptions and the selection of materials for the shaft. The final question was unclear and potentially related to the forces and deflection on the shaft caused by the centrifugal pump. Overall, the conversation touched on topics such as radial deflection, torsion, whirling, and hydraulic and mechanical unbalance.
billy_joule
This is a series of question that appear to become more and more vague, the last part has me stumped.

1. Homework Statement

A) I have an electric motor that produces 0.4 HP of shaft power at a speed of 2800rpm. What will the gearbox speed and torque be on the output of a 1:5 (in : out) gearbox? Assume a 96% efficient gearbox

B) design a shaft that is 100mm long to transmit the gearbox output torque of the above problem using sensible engineering assumptions. Select a material and design the diameter.

C) assume that you have a centrifugal pump impeller at the end of the shaft you designed in the above problem. What will be the maximum radial deflection at the tip of the centrifugal impeller with respect to the shaft? Assume that the impeller is rigid (does not deflect) and has a diameter of 100mm. Assume all deflection is from the 100mm long shaft only.

## The Attempt at a Solution

[/B]

Question A) is straight forward:
Poutput = Pin *η = 0.4HP * 0.96 = 0.384 HP

Rpmout = Rpm in * 5/1 = 14,000 RPM

HP = RPM* T / 5252

Tout = HPout*5252/RPM
= 0.386HP *5252 / 14,000 RPM = 0.1448 ft lbFor Question B), I think the simplest interpretation is "how thick must a solid shaft be to resist 0.1448 ft lb of torsion?"
I choose 316 SS (SS because it's for a pump, 316 because it's common) with yield stress of 205 MPa and a safety factor of 3.
So
0.1448 ft lb = 0.1963 Nm

τmax = 205 MPa/3 = 68.3 MPa
= (16x 0.1963 Nm / (π * 68.3 MPa) )1/3

= 2.446 mm

Which is expectedly thin, and such a slender shaft would likely undergo whirling before 14,000rpm.

Would the next step be to find the minimum diameter that gives a critical speed beyond 14,000rpm?
That would require some assumptions about how it's supported, simply supported at both ends would be the obvious assumption.

Part C) has me stumped:

What will be the maximum radial deflection at the tip of the centrifugal impeller with respect to the shaft? Assume that the impeller is rigid (does not deflect) and has a diameter of 100mm. Assume all deflection is from the 100mm long shaft only.

I would think the only radial stress would be due to the centrifugal force on the self weight of the shaft (and the blade weight if I estimated and included it).

Is it really asking me find the increase in radius of the shaft due to the speed of rotation?

I've only ever seen radial deflection in the context of pressure vessels & piping. I understand blade tip clearance is important but I'd assume the radial deflection of the shaft is inconsequential compared to the that of the blades themselves. Or is there some other interpretation?

The final question is practically gibberish . Even if we could put a meaningful interpretation on it there is still not enough data to get an answer .

The only thing that somewhat makes sense is that questioner is suggesting that CF pump is a crude single outlet type which discharges water tangentially to rotor . In that case rotor sees a torque and a radial load .

billy_joule said:
Is it really asking me find the increase in radius of the shaft due to the speed of rotation?

No, I think it is asking what force the fluid will exert upon the shaft.

This gives some idea of what it is all about.
http://www.mcnallyinstitute.com/06-html/6-5.html

Nidum said:
The final question is practically gibberish . Even if we could put a meaningful interpretation on it there is still not enough data to get an answer .

Thanks, that's what I thought. The problem is, this is a part of a 'take home test' for a graduate engineering role I interviewed for at a prestigious aerospace company, so it's particularly high stakes homework for me. At this point, I think It'll be better to skip it rather than plough through and get some result based on a string on assumptions.
256bits said:
No, I think it is asking what force the fluid will exert upon the shaft.

This gives some idea of what it is all about.
http://www.mcnallyinstitute.com/06-html/6-5.html

It seems the radial force (if any) depends on where on the pump curve the pump is operating, something I have absolutely no info on. I'd also need info on the geometry of the shaft support at the pump.

Any time a centrifugal pump operates away from its best efficiency point a radial force is generated that will attempt to bend the shaft. This can cause a rotating component, such as a wear ring or mechanical seal to contact a stationary component causing damage to either or both of them.

I know it says radial deflection but it could be loosely interpreted as torsion wise deflection - ie shaft twist . You have enough information to work that out properly .

In any case working out twist of a tentative shaft design to see if it is within safe limits would be a good thing to do .

Since your first shaft comes out at such small diameter you may like to choose a more generous size based on ' engineering judgement ' and give an explanation of reasons in your answer .

You could also give a descriptive account of concerns about whirling and hydraulic and mechanical unbalance .

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billy_joule said:
It seems the radial force (if any) depends on where on the pump curve the pump is operating, something I have absolutely no info on. I'd also need info on the geometry of the shaft support at the pump.

Not all impellers are enclosed within a housing.

I gave you the reference so as to give you the ability to reflect upon on how a radial deflection can occur.

There are many tools and industrial applications where it would be desirable to know the deflection and forces on a shaft. Circular sanders, drill bits, agitators, are just a few examples where the working part of the tool is supported only on one end. The defection can be caused by the production of pressure difference across the tool end, by encountering different properties of the working material, by movement of the tool itself.

billy_joule said:
It seems the radial force (if any) depends on where on the pump curve the pump is operating, something I have absolutely no info on. I'd also need info on the geometry of the shaft support at the pump.
In that instance yes. You also have no information on the working fluid. It could be viscous such as concrete mixture, or a more freely flowing such as water. The article does though give you the fact that if optimally operating the shaft "should" experience no deviance from perfect rotation. The problem also does not give you the mass of the impeller and related to determine dynamics and harmonics.
billy_joule said:
Thanks, that's what I thought. The problem is, this is a part of a 'take home test' for a graduate engineering role I interviewed for at a prestigious aerospace company, so it's particularly high stakes homework for me. At this point, I think It'll be better to skip it rather than plough through and get some result based on a string on assumptions.
Sorry, but that is a cop out. Engineering is based on assumptions that try to model the real world on what facts are available.
The prestigious aerospace company may decide one day to enter into a design of a drill to be part of an endeavor for asteroid mining, and need to ensure that their drill, when sent up to the asteroid does its job. You are asked by your supervisor.to determine the maximum deflection of the drill bit.

You have one piece of given information with which you can determine a deflection. That is the torque.

256bits said:
You have one piece of given information with which you can determine a deflection. That is the torque.

I ended up calculating the arc length the impeller tip traverses due to the shaft twist and justified why I did so rather than try to find a radial deflection.
I also checked if the shaft was at risk of whirling, it wasn't.
I appreciate the responses, good advice.

billy_joule said:
I ended up calculating the arc length the impeller tip traverses due to the shaft twist and justified why I did so rather than try to find a radial deflection.
I also checked if the shaft was at risk of whirling, it wasn't.
I appreciate the responses, good advice.

Shaft twist is not radial deflection. That is not what is asked, no matter what explanation give.

Why have you not considered the simple answer with what happens if a blade tip binds against a surface and stops turning?

256bits said:
Why have you not considered the simple answer with what happens if a blade tip binds against a surface and stops turning?
Short of a foreign object entering the pump, isn't radial deflection a prerequisite for binding?
And if binding did occur, wouldn't it be a constraint on radial deflection?

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You could do a limit state case where the impeller is assumed to be reacting all the pumping load on one side only and at maximum radius . No explanation need be given except that this is worst possible case . Radial load on shaft is then determinate and beam wise deflection of shaft can be worked out .

It did occur to me overnight that question part 3 might be an initiative test . Engineering problems often have to be solved where there is insufficient data and questioner might just be seeing what you make of a partially defined problem .

More generally the concept of limit state analysis of structural problems or indeed many other problems is a very powerful tool though little used and seldom taught .

Nidum said:
It did occur to me overnight that question part 3 might be an initiative test . Engineering problems often have to be solved where there is insufficient data and questioner might just be seeing what you make of a partially defined problem .

I would tend to agree.
If parts A and B would be worth 10 points each, Part C in relation would be 80 points.

billy_joule said:
Short of a foreign object entering the pump, isn't radial deflection a prerequisite for binding?
And if binding did occur, wouldn't it be a constraint on radial deflection?

Kind of a catch 22 isn't it.

I'll try to get back as soon as possible

## 1. What is radial deflection of a rotating shaft?

Radial deflection of a rotating shaft is the measurement of the amount that the shaft bends or flexes perpendicular to its axis of rotation. This can occur due to various factors such as uneven distribution of weight, external forces, or improper alignment.

## 2. How is radial deflection measured?

Radial deflection is typically measured using specialized instruments such as dial indicators or laser alignment tools. These tools allow for precise measurement of the amount of deflection in millimeters or inches.

## 3. What factors can contribute to radial deflection?

Several factors can contribute to radial deflection, including the weight and distribution of the material being rotated, the speed of rotation, and any external forces applied to the shaft. Improper alignment or uneven wear can also cause radial deflection.

## 4. What are the potential consequences of excessive radial deflection?

If left unchecked, excessive radial deflection can lead to increased vibration, wear and tear on the shaft and surrounding components, and even failure of the rotating equipment. It is important to regularly monitor and address any excessive deflection to prevent these potential consequences.

## 5. How can radial deflection be mitigated?

Radial deflection can be mitigated by properly aligning the rotating shaft, evenly distributing the weight of the material being rotated, and minimizing external forces. Regular maintenance and monitoring can also help identify and address any potential issues before they become significant.

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