Surface area of a cylindrical rigid rod

Basically , I have two rods of 1cm diameter and 5 cm height. One of the rods is fabricated in such a way that a helical thread is created throughout the rod with a helix angle of 60° . Other rod is fabricated in such a way that the surface is diamond grit knurled throughout.

So this is done to increase the surface area compared to the smooth rod.

My question is that I want to find the surface area of each of the rods .

I hope someone could help me with this.

Thank you so much.

Zaqf said:

Basically , I have two rods of 1cm diameter and 5 cm height. One of the rods is fabricated in such a way that a helical thread is created throughout the rod with a helix angle of 60° . Other rod is fabricated in such a way that the surface is diamond grit knurled throughout.

So this is done to increase the surface area compared to the smooth rod.

My question is that I want to find the surface area of each of the rods .

I hope someone could help me with this.

Thank you so much.

Click to expand...

This is a terrific geometric question.

However do you really need the explicit surface areas ?

OR

would the ratio of the difference of surface areas be sufficient ?

AND ---> To what "Precision" do you need to know the difference in surface areas to ? 98% accuracy 99.9999 % accuracy ?

Just helps to know in terms of engineering requirement how accurately the surfaces are modelled and computed / calculated (mathematically). How far one goes to describe intricate 3 dimensional surface features. And derive various formulae accordingly.

What is the profile of the thread (for the 60 degree helix angle ) ? Is it just a single thread ?

Rough indication of "Depth" of knurl and intended geometry of diamond knurl ?

What is the application ?

What is the lesson plan ?

Draw them on CAD and measure ?

Diameter X "pi" X length. Pi is like 3.142

so - YOUR rod has an area of 5 X 3.142 = 15.71 Cm

You did not include ANY info on the physical properties of your processing, so , no, we have no idea of the "adder" of any such process

Maybe if you immerse both rods in a salt solution, any strength common salt, measure the resistance of each, rod-to-solution with an Ohmeter. The surface area of each should be in the inverse ratio of their 'resistance'. Now do the simple calculation of the area of the plain rod .. multiply that by the inverse ratio of the resistances & you'll have the surface area of the 'improved surface' rod. All assuming conductive (metal) rods. Not sure if it would work best with rather dilute salt solution or concentrated. Done in a big bucket would be best with the rod & other Ohmeter probe far apart to avoid 'throwing power' problems.

.... or possibly machine one each out of aluminum, add a temp prob to a hole in each one. Place them in an oven and track temp increase over time? Or possible do the same test dunking the into a bucket of ice/water.

PM

Posted by Daniel Livshitz on finishing.com in 2003 (I think): electroless nickel plate the rod together with a thin square sheet of the same material for the same time, having weighed both beforehand. After plating weigh each & determine the weight increase of each. The square sheet area is easily calculated (both sides). Simply divide the weight increase of the rod by that of the sheet & multiply by the surface area of the sheet. This is paraphrased not verbatim. Obviously electroless nickel is most able to give a uniform coating not dependent on throwing power.

I would model them in Solidworks and use the Mass Properties function, which will tell you an accurate surface area.

mhajicek said:

I would model them in Solidworks and use the Mass Properties function, which will tell you an accurate surface area.

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or any decent cad program. software has made us lazy, but I do not have time for the fun geometry maths with work and all.

memphisjed said:

or any decent cad program. software has made us lazy, but I do not have time for the fun geometry maths with work and all.

Click to expand...

I'd take a pretty good stab at it mathematically and attempt to reduce it to something simple ~ The non CAD version with "inky" drawings etc. lol. ('cuz hand made stuff that's not CAD / CGI is cool now - back in fashion ;-) and technically we're (our little group) not allowed to publicly puke up CAD renderings / drawings on the interwebs - difficult line to "Draw".)

BUT OP has not come back with basic "Parameters". So starting off with random initial assumptions IS a huge waste of time.

annnnnnnd, OP double posted the same thread into the general forum …

Surface area of a cylindrical rigid rod

(This forum doesn't have the fancy linking capability that other forums have, nor have I seen a concatenated thread ? here ? ).

Oh well ¯\_(ツ)_/¯

I like the ideas various people have tossed out. Ni plating is really cute but requires a rather good analytical balance to execute.
The thermal probe is going to give you an exponential curve to equilibrium. somewhat of moving target but possible.

Using them as electrodes in a conductive solution is a definite possibility but you will get surface hydrogen build up so constant changing value. Connecting them as a bridge would help the sensitivity of the test and give you a ratio of the areas.

Certainly if you have Solidworks or something else that will model the surface that is the simplest way.

However Google is your friend: area of rt regular pyramid. The formula I found included the base area so drop the length x width term. Clearly dividing by l*w will give you a ratio for base area to area of the triangles.

Easy or hard; pick your poison.

I was bored so I modeled these in FreeCAD, but I couldn't find a "properties" type dialog in FreeCAD so I imported them to F360. First is plain cylinder, second is threaded to M10x0.5, and the third is a 16 TPI diamond knurl as per ISO13444.

GenePoole said:

I was bored so I modeled these in FreeCAD, but I couldn't find a "properties" type dialog in FreeCAD so I imported them to F360. First is plain cylinder, second is threaded to M10x0.5, and the third is a 16 TPI diamond knurl as per ISO13444.

Click to expand...

That's pretty nice...

Does the surface area calculation include the circular "end caps" for the volume (modelled enclosed "solid") ? Or were you able to select just the cylindrical surface ? ~ My hunch is that's more relevant to OP's idea - maybe ???? (i.e. do you have to subtract the area of the ends ?).

I think OP said 60 degree helix angle for thread but didn't indicate number of threads nor profile ?

very interesting

I was thinking of working different sizes and geometries to derive a more universal algorithm with different use case precisions.

Like what is the difference if the cross sectional radii become progressively larger, what happens when you tend to a near infinite radius (do you reach some kind of asymptote or constant ? ) + formulae derived from different ways to "Unwrap" the surface. Effects of different "depths" of knurl, light versus deep on surface area. etc. + different types of knurl/ pattern.

Knurling is interesting in terms of near constant volume. versus an actual cut that removes material as in threaded features ?

I was wondering if OP meant to create an alternate knurling pattern using left and right handed threading techniques and compares the two ???

Yes it would include the ends in the calculations, all he would have to do is delete the two end faces and it would become a surface model and then you'd get the correct surface area of the cylinder.