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Determine the Diameter of a Shaft Based on Torque and RPM

09/20/2017 8:27 AM

This motor will spin at 85RPM delivering 1255Nm of torque.

Force = 1255Nm = 1.255*10^6Nmm^2

Modulus of Elasticity = 205 GPa

Poissons Ratio = 0.29

Modulus of Rigidity = 205/(2*(1+0.29)) or 79.457

I know the formula:

T/J = Fs/R (this might be a big oversight on my part but how do I calculate the shear stress, so that I can solve for the diameter?

1.255*10^6/ (PI/32)*D^4 = Fs/(D/2)

I feel like I have everything that I need but I just can't seem to put it together properly to solve my problem. How do I get the shear stress to calculate the needed diameter that will support this amount of torque?

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#1

Re: Determine the diamater of a shaft based on Torque and RPM

09/20/2017 8:30 AM

Still having problems?

What is the diameter of the output shaft of the motor?

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#2
In reply to #1

Re: Determine the diamater of a shaft based on Torque and RPM

09/20/2017 8:58 AM

Yes, still having issues as I feel like I am going in circles.The output shaft on the motor is 6cm with a 1/2cm key.

I have all these formulas on paper but I can't seem to put it together in a coherent way to solve my problem.

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#3
In reply to #2

Re: Determine the diamater of a shaft based on Torque and RPM

09/20/2017 9:01 AM

So work backwards: assess whether a <...6cm...> shaft is adequate.

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#21
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Re: Determine the diamater of a shaft based on Torque and RPM

09/21/2017 6:10 AM

Without appearing to be "too pedantic," in engineering, preferred dimensions are metres (m) or, millimetres (mm), not cm......cm's are used in the clothing industry because of the women's lobby........mm's made their measurements sound "too big".......so I am led to believe. In 1965, the year before Australia changed to the metric system, a teaching colleague and I converted all South Australian TAFE engineering books to metric, including all the formulae. In the Système International d’Unités (which was adopted in Australia) all dimensions, capacities etc., have preferred units and these are the units that should be used.

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#22
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Re: Determine the diamater of a shaft based on Torque and RPM

09/21/2017 6:25 AM

That's right, preferred measurements are in multiples of 1000, but bar (105Pa) is the exception that proves the rule! And it's too convenient a unit to give up.

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#26
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Re: Determine the diamater of a shaft based on Torque and RPM

09/21/2017 8:43 AM

Similarly in nautical measurements, nautical miles are used for distance and knots for speed.........not good to shorten nautical miles to nm.........could be confused by some to be Newton metres even though that is Nm.

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#31
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Re: Determine the diamater of a shaft based on Torque and RPM

09/21/2017 9:52 AM

nm could also be nano-meters.

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#33
In reply to #21

Re: Determine the diamater of a shaft based on Torque and RPM

09/21/2017 10:43 AM

A question:

" cm's are used in the clothing industry because of the women's lobby " .

I went to Google and looked up, " women's lobby, that led me to : the Australian Women's Lobby. I had previously thought that all clothing measurements were in : inches.

Then I looked on Google and went to a bridal wear fabricator in Great Yarmouth, UK ( Catrina's Bridal wear ) and on their website, the measurements are in inches.

Then I went to Google and entered: Women's clothing measurements in u.s. . The chart listed measurements in both inches & centimeters.

This site listed an acronym: asos.

Then I went to Google to see what asos meant, to see how asos relates to Women's clothing measurements.

Could you specify how, why or where asos has been adopted by the Australian clothing industry ?

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#43
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Re: Determine the diamater of a shaft based on Torque and RPM

09/22/2017 12:34 PM

As I pointed out "it was something that I was led to believe".........I am not sure how accurate it was........didn't have a computer back in those days to check statements like that, but, it did sound plausible!!!

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#38
In reply to #21

Re: Determine the diamater of a shaft based on Torque and RPM

09/21/2017 8:18 PM

I typically used mm but I have no idea why I wrote this one in cm. Either way, thanks for the insight and history lesson, good info to know, plus you can never be too pedantic with me.

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#40
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Re: Determine the diamater of a shaft based on Torque and RPM

09/21/2017 11:43 PM

.........you can never be too pedantic with me.

That's good to know marlons and I certainly appreciate your comment.

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#4

Re: Determine the diamater of a shaft based on Torque and RPM

09/20/2017 9:07 AM

Try here.

This may help you also.

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#5
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Re: Determine the diamater of a shaft based on Torque and RPM

09/20/2017 9:55 AM

I think the first post might have helped me. It seems that shear stress is basically the modulus of rigidity; which I calculated in the original post. Why does things have to be called by so many different names?

This might seem like a simple question but knowing the force 1255Nm how do I calculate the shear stress?

It seems like it leads me back to this equation:

τ = T r / J

τ = 1.255x10^6Nmm^2 * r / J

J for a solid shaft is PI*D^4/32, so

τ = ((1.255x10^6Nmm^2) * (D/2)) / ((PI*D^4)/32)

But again I am missing shear stress and Radius.... I bet I am overlooking something simple but I've been staring at these equations too long.

What am I doing wrong up above?

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#50
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Re: Determine the diamater of a shaft based on Torque and RPM

10/04/2017 9:54 AM

Shear stress is not modulus of rigidity. Stress is force, strain is the response of a material to this force (displacement). Modulus of rigidity is shear stress divided by shear strain. It has the same units as stress because strain is a dimensionless quantity (length/length).

http://www.engineeringtoolbox.com/modulus-rigidity-d_946.html

1 pascal = 1 N/m2

If the modulus of rigidity if steel is 80 x 109 pascals this means that if you have a block of steel 1 cubic meter and apply a horizontal force to the top of 1 Newton, that the top will be displaced in the direction of force a distance of 1 / 80 x 109 or 1.25 x 10-11 meters.

When you apply a torque to a shaft, there is shear stress that increases from zero at the axis to a maximum at the outside.

http://www.pricoltech.com/torsional-analysis-of-a-circular-shaft/

τ = T r / J

τ is shear stress,

T is torque applied to shaft,

r is the distance from the center,

J is the Polar Moment of Inertia (proportional to 4th power of shaft size)

The shear stress of a shaft with Polar Moment of Inertia J with a torque T applied has a shear stress τ at distance from the center r. So, the maximum shear stress is where r = D/2, the outside of the shaft.

The larger the shaft, the greater J is and the smaller the stress τ is at any given distance from the center. If the shaft is small, J is very small, the shaft will twist (torsion) or the stress will exceed the strength of the material and the shaft will break.

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#51
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Re: Determine the diamater of a shaft based on Torque and RPM

10/04/2017 10:18 AM

You are an excellent teacher old buddy!

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#52
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Re: Determine the diamater of a shaft based on Torque and RPM

10/04/2017 11:48 AM

We've told him most of that a number of times. If it hasn't sunk in yet I doubt if it ever will.

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#53
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Re: Determine the diamater of a shaft based on Torque and RPM

10/05/2017 3:51 AM

Sorry!! Could you please repeat that........I didn't hear it!!!

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#54
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Re: Determine the diamater of a shaft based on Torque and RPM

10/05/2017 4:06 AM

LOL! Neither did marlons it seems

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#55
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Re: Determine the diamater of a shaft based on Torque and RPM

10/05/2017 4:35 AM

That reminds of a saying I used to use regularly to some of the students I used to teach.........."You can tell them anything, but, you can't tell them much"

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#56
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Re: Determine the diamater of a shaft based on Torque and RPM

10/05/2017 5:16 AM

Reminds me of a saying about the Metropolitan police in London - you can always tell a Met man, but not much.

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#57
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Re: Determine the diamater of a shaft based on Torque and RPM

10/05/2017 5:27 AM

This is also true.........being a "pom" from waaaay back. I was 10 when I came out to Oz, I am now 77 (Sunset Strip......not for a while yet, I hope........my mother is 97 and still looks after herself.....HOPE I have her genes)

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#58
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Re: Determine the diamater of a shaft based on Torque and RPM

10/05/2017 11:27 AM

...or tell much about them either!

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#6

Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/20/2017 11:08 AM

I don't see what RPM has to do with anything...

The motor supplies some torque which results in torsion of the shaft (amount of twist per unit length) which depends on the torque, the diameter of the shaft, and the material properties of the shaft.

I am assuming that you want to calculate the torsion and maximum stress...

Here is an example that you might want to follow to understand the process:

Example - Shear Stress and Angular Deflection in a Solid Cylinder

A moment of 1000 Nm is acting on a solid cylinder shaft with diameter 50 mm (0.05 m) and length 1 m. The shaft is made in steel with modulus of rigidity79 GPa (79 109 Pa).

Maximum shear stress can be calculated as

τmax = T r / J

= T (D / 2) / (π D4 / 32)

= (1000 Nm) ((0.05 m) / 2) / (π (0.05 m)4 / 32)

= 40764331 Pa

= 40.8 MPa

The angular deflection of the shaft can be calculated as

θ = L T / (J G)

= L T / ((π D4 / 32) G)

= (1 m) (1000 Nm) / ((π (0.05 m)4 / 32) (79 109 Pa))

= 0.021 (radians)

= 1.2 o

http://engineersedge.com/calculators/torsional-stress-calculator.htm

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#15
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/20/2017 4:53 PM

This is a good answer but this assumed that I already know the width of the shaft.

I do not.

This is what I would like to calculate based on the input torque 1255Nm And the material properties.

I calculated that the modulus of rigidity = 80GPa

Torque is above and I know the formula for polar moment of inertia.

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#17
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/20/2017 11:49 PM

How does me trying to clarify the question get voted as off topic?

That's why I had the rpm in the first post.

If I know the torque and rpm that the shaft need to operate at, can I calculate the diameter of the shaft?

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#24
In reply to #15

Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/21/2017 7:06 AM

If you don't like the 40.8GPa max shear stress, try a different diameter. What's hard about that?

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#28
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/21/2017 9:05 AM

".........width of the shaft"

Is that length or diameter of the shaft???

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#32
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/21/2017 9:54 AM

Seems to be something in the eye of the beholder now doesn't it?

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#23
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/21/2017 6:31 AM

If I may make a suggestion Rixter........it is always more convenient to work this type of problem, in metric units, to use Newtons (which you did), but, dimensions in mm's, you then end up in MPa......... there are only two things that annoy me with the Système International d’Unités.......(1) Pascal......it is such a small unit, I understand it as a base unit, but, not a preferred unit and (2) Hertz..........cycles/second meant something, you could see it on a cro, or similar, but, Hertz????

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#25
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/21/2017 7:38 AM

SI may not be perfect, but it's a great deal better than the alternatives - cgs, fps.

Metric bolting is another godsend, after years of struggling with BSF, BSW, BA, UNF, UNC etc.

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#27
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/21/2017 8:56 AM

Could not agree more........as I said in my previous I only had "problems" with Pa (imagine, a force of 1 Newton applied over an area of 1m2) and Hertz (does not conjure up anything in the mind), but, I can certainly live with them..........as you said metric fasteners are "magnifique"

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#7

Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/20/2017 11:22 AM

https://skyciv.com/free-shaft-calculator/

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#8

Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/20/2017 11:54 AM

D = 1.72 (Tmax/σmax)1/3 (4)
Reference https://www.physicsforums.com/threads/torsion-of-shafts.131292/

from one of JPool's links.

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#16
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/20/2017 5:58 PM

Can I design a solid shaft diameter based on expected input force and rpm?

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#19
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/21/2017 3:53 AM

Isn't the need for help with that assessment the actual reason for the original post?

How confusing.

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#29
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/21/2017 9:49 AM

I don't know, can you? Is algebra an issue here? You have been provided all manner of links and formulae, so go at it, and tell us what you did, your answer, and if it worked.

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#41
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/21/2017 11:48 PM

The way this discussion is going I reckon the shaft may get "broke" .....and then it will really need "fixing"

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#34
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/21/2017 12:07 PM

I read that thread and that OP seems like me from the past, that's the exact same questions that I had and felt the exact same way.

What they are basically saying is that σmax doesn't even need to be max but just σ and in this case I can use the tensile yield strength of the material from the material sheet? Which in this instance is 490MPa then I can solve this equation [τ = T r / J] for r to get my answer?

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#35
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/21/2017 12:18 PM

I believe so, then allowances for whatever start-up or instant lock transient that could ever transpire, please be aware that torque might go through the roof on lock up.

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#36
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/21/2017 12:32 PM

If you think you can use the tensile yield strength for design shear stress, you've got a lot to learn.

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#37
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/21/2017 1:39 PM

He is wanting to make twisty steel, it is all the rage now.

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#39
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/21/2017 8:27 PM

You are right about not using the tensile strength per se, I have to use the modulus of rigidity which is 80MPa in this material but I should also reduce that number by some factor of safety.

So it's not the Yield tensile strength but I should use the Modulus of rigidity as τ in this formula: τ = T r / J and solve for r.

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#42
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/22/2017 4:36 AM

Just once more. Yield strength doesn't come into your formula. Your formula calculates the actual stress τ, which you compare with yield strength to decide whether your calculated τ is acceptable. As I've said before, I can't tell you what τ is acceptable. I'm not a rotating machinery man. In structural steelwork design, shear stresses are weighted more heavily than tensile in finding effective total stress, probably similar for shafts. So you need a substantial safety factor.

Modulus of rigidity doesn't come into the stress calc, only the angular twist (been there before too).

BTW, in your #5, didn't it occur to you that r = D/2?

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#9

Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/20/2017 11:56 AM

Determine the Diameter of a Shaft Based on Torque and RPM ...

What is the mane of this class you are having difficulty with?

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#10
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/20/2017 12:19 PM

His perfesser must be Dr. Lions.

LOL the mane of the class..

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#11
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/20/2017 12:52 PM

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#13
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/20/2017 1:30 PM

Is that Clarence, except must be his non-cross-eyed son!

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#12

Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/20/2017 12:54 PM

You forgot to say what color it is.

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#14
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/20/2017 1:31 PM

I would think he should use the one with the blue dot of spray paint on the end of the shaft.

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#18
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/21/2017 3:09 AM

Paint in black?

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#30
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/21/2017 9:50 AM

Nah, black is not good paint for motor shaft. Maybe spiral stripes so one can see it spinning.

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#20

Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/21/2017 4:28 AM

What's the problem now? We've been through this several times.

You've got it all in the last equation in your post. You can select a suitable Fs (we've been there as well) and solve for D, then use next bigger standard size, or solve for Fs and try various D figures to get an acceptable Fs.

As I said in earlier thread, I can't tell you what an acceptable Fs is, perhaps other posters will suggest a figure.

Modulus of elasticity and rigidity don't come into into directly. It might be worth checking the angular deflection, but unlikely to be excessive if Fs is moderate.

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#44

Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/27/2017 1:08 PM

I had some technical difficulties this past week and wasn't able to get back online. I have been thinking about this problem though and wanted to run this by the forum before I proceeded to apply algebra to it. Also keeping things simple and avoiding factor of safety for now.

The formula for torsion in a shaft is: τ = T r / J

Since I would like to design for the shaft size based on data I have on hand which is:

Torque = 1255Nm

Modulus of rigidity = 80GPa

Polar moment of In. = PI* R^2 / 2

The way to choose a shaft size for basic transmission shaft would be:

80GPa = 1255Nm * (R) / (PI* R^2 / 2)

Then solve for R?

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#45
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/27/2017 1:52 PM

Yes, basically, but you have to convert your units to basic units in terms of, Kg, m, s.

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#46
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/27/2017 2:31 PM

NO! That's wrong. I and others have tried hard to help you with any number of posts but you clearly haven't understood. Go back and try again.

"The formula for torsion in a shaft is:" τ = T r / J. No! That's the formula for shear stress τ when torque = T. And it's not the same as the modulus of rigidity, though they have same units. Modulus of rigidity only relates to angular deflection, as has been said more than once, and allowable stress is a factor something like 1000 smaller.

"Polar moment of In. = PI* R^2 / 2" is wrong, it should be pi*R4/2. That's probably a typo on your part, but it makes a big difference.

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#47
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/27/2017 3:20 PM

What you said. I know I did this once in freshman Physics, but I am old now. That is my excuse, so I am without one.

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#48
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/27/2017 9:16 PM

Welcome to the era of old age and "seniors moments"...........always helpful to say:

"Oh! I am sorry, I must have had a seniors moment"

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#49
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

09/28/2017 11:32 AM

Then I would spend all day apologizing, so I tread onward, with bluster, and I forgot the other "B" word I was going to use. Sorry, senior moment!

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#59

Re: Determine the Diameter of a Shaft Based on Torque and RPM

10/05/2017 12:14 PM

I spent some time actually looking into this stuff some more.

The saddest part of this whole physics game is that, it's just that a game. With all the complicated formulas and such everything is just a derivative of the tensile strength test.

I figured out what I needed to know and I am more than a little disappointed in the whole affair. It made sense to you guys because you're steeped in in.

It doesn't make sense to the average guy because it's all Greek letters, chants, dances and a big does of prayer and don't forget the large factor of safety.

I guess it's about how much risk you're willing to take when u fill in your spreadsheets. Thanks for all the help, I got it now.

p.s.

The reason your students wouldn't listen is because they most likely could smell the foul odor of b.s. I'm not saying your a bad person or anything like that but when physics says in one breathe; it's just an approximation but then in the next breathe but it's real you have to wonder does that person suffer from some mental disorder.

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#60
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

10/05/2017 12:29 PM

If you know the property of the steel, the size of the steel, and the torque to be applied to the driven object, how can you possibly miss the answer?

the bigger shaft wins. Make an allowance and move on.

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#61
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

10/05/2017 1:06 PM

I don't know who that's addressed to, but you're not the only one who's disappointed. We've told you how to do it several times, but you either didn't study the answers or didn't understand, and then repeat the question.

The concepts and formulas used here are about as simple as you could hope for in any branch of engineering. If you have trouble with them maybe you should be looking at a different field.

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#62
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

10/05/2017 1:42 PM

I think I will start a thread asking how to make my flying Jetson car, and when you give me the answer I will say, but I want to calculate it using just the weight, and forget the lift.

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#63

Re: Determine the Diameter of a Shaft Based on Torque and RPM

10/05/2017 1:50 PM

If you're not sure who it's addressed to then obviously not you.

Anyways like I said I figured it out, thanks for making it so simple...

Physics

goodbye Engineering 360, time well wasted.

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#64
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

10/05/2017 1:59 PM

I suspect that no matter where you, there you will be found. Nothing will change in your life unless you take responsibility and change it.

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#65
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

10/05/2017 2:31 PM

I didn't think it was addressed to me, but the fact that I wasn't sure doesn't make it obvious, as far as I can see.

Good luck in your chosen career.

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#66
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Re: Determine the Diameter of a Shaft Based on Torque and RPM

10/05/2017 6:56 PM

Consider yourself told!!!!

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