Misc. Home project - rotary table calculations

[nvn]

dislect: D in the denominator of y_a is not your D. See p. 457. You will need to give their D a different name, since you are already using the name D.

Your answers for C3 and L3 are currently incorrect. You forgot to multiply by the beginning coefficient, before the braces. Try again. Also, I was not able to obtain your w value yet.

By the way, generally always maintain four significant digits throughout all your intermediate calculations, then round only the final answer to three significant digits.

You do not need the pipe length to obtain the axial force on the vertical pipes.

 

[dislect]

dislect: D in the denominator of y_a is not your D. See p. 457. You will need to give their D a different name, since you are already using the name D.

Your answers for C3 and L3 are currently incorrect. You forgot to multiply by the beginning coefficient, before the braces. Try again. Also, I was not able to obtain your w value yet.

By the way, generally always maintain four significant digits throughout all your intermediate calculations, then round only the final answer to three significant digits.

You do not need the pipe length to obtain the axial force on the vertical pipes.

- My a=1000mm, b=85mm, r0=750mm
I corrected D, using E=69 GPa. thanks for noticing !
Corrected calculation but still result is way too high :

http://www.siz.co.il/my/tdzh4aw2lzyi.png -- About the support leg pipes,
1. I tried calculating the minimum x distance between the 4 legs and came up with a result that seems a bit big, plus as written in green in the picture its weird that if i reduce the number of legs i actually minimize the distance x ?
Also, it seems like the dimensions of the pipes barely make a difference on the end result even with t2=0 (full pipe)

http://www.siz.co.il/my/tayjnd0jn1em.png

2.what about calculating the bend momentum and the center of the pipe (L/2) to see if it breaks at the weakest spot and how much it bends due to the momentum of the weights + table mass?I know it's a lot but I'm really feeling like I made progress thanks to your help, getting there really fast now!

 

[Engineer_Phil]

You should also check for buckling of the leg(s). If the slenderness ratio is high enough the legs will buckle well below the listed yield strength of the material.

 

[nvn]

dislect: Your value for E is correct in the text of post 32, but wrong in your first attached file. Check your units. And you did not update C3 and L3 in your y_a equation. Let's see if that gets you closer on your first attached file. I will review your second attached file within one day.

I could not exactly match your M_table (nor w) answer yet. I do not know if you are using some strange value for pi, or something like that.

By the way, list four significant digits for each intermediate value. Leading zeros do not count as significant digits. E.g., list 0.002251 for L3, four significant digits, not 0.002, which is only one significant digit. As another example, list 0.2393 for C2, not 0.239.

 

[dislect]

dislect: Your value for E is correct in the text of post 32, but wrong in your first attached file. Check your units. And you did not update C3 and L3 in your y_a equation. Let's see if that gets you closer on your first attached file. I will review your second attached file within one day.

I could not exactly match your M_table (nor w) answer yet. I do not know if you are using some strange value for pi, or something like that.

By the way, list four significant digits for each intermediate value. Leading zeros do not count as significant digits. E.g., list 0.002251 for L3, four significant digits, not 0.002, which is only one significant digit. As another example, list 0.2393 for C2, not 0.239.

E: I am using E=69 GPA which as i checked it 69 * 10^6 [N/m] and for the calculation of D i used meter instead of mm, so i converted 10mm^3 to 0.01m^3 and came up with the result written. When i used it in y_a equation i went back to mm so i multiplied by 1000. Did i do something wrong?
C3 & L3: I updated the values and my y_a is now - 10,701 mm ... still doesn't make sense.
M_table : 83.6 kg total ; so every 45 degree section of the table is m1*=20 kg + 83.6/8 kg = 30.45 kg and then i use it to calculate w*=0.507 [N/mm]

 

[nvn]

dislect: 69 GPa is not 69e6 Pa. Try again. (By the way, do not worry too much yet about analyzing the pipes. First, get the preliminary things computed correctly.)

 

[dislect]

dislect: 69 GPa is not 69e6 Pa. Try again. (By the way, do not worry too much yet about analyzing the pipes. First, get the preliminary things computed correctly.)

I see, its suppose to be 69e9 Pa so now my deflection is -10.701 mm which is a lot better but still seems to be quite large, right? I would expect less than 1mm
If all calculations are correct I need to increase the table thickness from 10mm to around 50mm to get a small deflection

 

[nvn]

dislect: The equation you listed for M_table gives 84.21 kg, instead of 83.6 kg. I do not know how you got 83.6 kg.

Your answer for y_a is close to the correct answer. It might be inaccurate by approximately 0.8 %. I am not sure why. Could it be because you did not maintain four significant digits throughout your calculations? Anyway, it is close to correct.

So, you computed y_a essentially correctly. Do you think you would find a deflection of -10.7 mm acceptable?

The P2 equation is developed only for the pipe configuration shown in your diagram in post 14. Therefore, you should divide the P1 numerator only by 4, not 3.

Your A3 formula is wrong; the "t" is wrong. Try again.

In your second attached file, after you changed the absolute value to positive, did -298.71 become positive? If so, what should happen to it when you move it to the other side of the less-than sign? Try again.

 

[dislect]

I'm still getting M_table 83.6 kg
http://www.siz.co.il/view/m1umit2zdy2t.png.htm
my y_a gives me a deflection angle of 0.6 degree so i think i can live with that :) thanks!

A3 formula: is it suppose to be -2t? i corrected it, but it doesn't make much of a difference.
I also used the 155 MPa as is and did not convert to Pa, so now i need to multiply by 1000000?
I corrected the sign of 298.71, multiply by 155 MPa by1000000 and now the end result is:
http://www.siz.co.il/view/gfigi3wlfynn.png.htm
http://www.siz.co.il/my/gfigi3wlfynn.png

That's still weird because the radius of each pipe alone is 20mm

 

[nvn]

dislect: In your M_table equation, I now noticed, you forgot to square the 2 in your denominator. Try again.

Your A3 formula change to -2*t2 is correct. Your answer for x is correct. Excellent work.

Therefore, this is telling you, any x > 7.7 mm is, so far, OK for your current pipes. Therefore, choose the pipe size and pipe spacing you prefer. And you can check Rty3 again. And then you will obtain your P3 value. Therefore, post all of this, and then I will get back with you within one day, to address your other question in post 32.

 

[dislect]

dislect: In your M_table equation, I now noticed, you forgot to square the 2 in your denominator. Try again.

Your A3 formula change to -2*t2 is correct. Your answer for x is correct. Excellent work.

Therefore, this is telling you, any x > 7.7 mm is, so far, OK for your current pipes. Therefore, choose the pipe size and pipe spacing you prefer. And you can check Rty3 again. And then you will obtain your P3 value. Therefore, post all of this, and then I will get back with you within one day, to address your other question in post 32.

Thanks!
I now chose x=40cm and calculate my Rty3=2.47% which is great!

Can't wait to get to post 32 thanks for the help!

 

[nvn]

dislect: And I forgot to add, also post your pipe length.

 

[dislect]

dislect: And I forgot to add, also post your pipe length.

Pipe length is L=80 cm

 

[nvn]

dislect: What is the material of your pipes?

 

[dislect]

dislect: What is the material of your pipes?

aluminium 1060

 

[nvn]

dislect: What is the heat treatment condition (also sometimes called temper) of your Al 1060 pipes? And do you already have the tensile modulus of elasticity (E2), tensile ultimate strength (Stu2), and tensile yield strength (Sty2) of this alloy, in MPa? Do you have a material specification name or number?

What is your table top aluminum alloy and temper?

 

[dislect]

dislect: What is the heat treatment condition (also sometimes called temper) of your Al 1060 pipes? And do you already have the tensile modulus of elasticity (E2), tensile ultimate strength (Stu2), and tensile yield strength (Sty2) of this alloy, in MPa? Do you have a material specification name or number?

What is your table top aluminum alloy and temper?

Hi, its:

But we can just leave it as variables for the moment and create the equations, i prefer it that way

 

[nvn]

dislect: Your current material is different from what I initially assumed. Therefore, if you are sure your post 47 material properties are correct, then go back and change your Sta value, throughout all of your analyses, to Sta = 67.0 MPa.

Your vertical leg pipes are currently fine, so far. Buckling is no issue whatsoever for your current leg pipes, and you do not need to worry about it at all. There is currently essentially no bending stress on the vertical leg pipes, coming from the table top, so far; therefore, there is no bending stress to check, so far. Due to the weights on the table top, the vertical pipes are currently subjected to only axial load (P3), and uniform axial stress (sigma3), which is very low, which you have checked.

One of the next things we might need to consider is, if someone twists your table top, torsionally, then will your vertical leg pipes be too flexible? If so, you might need to add partial shear panels between the vertical pipes (or perhaps diagonal members, or stiffener plates), to reduce torsional deflection.

 

[dislect]

I'll update what's needed.

Thank a lot for your help! almost done calculating

About the twist i don't think its something to worry about because the table is mounted on top of a thrust bearing which is placed in the stand supported by the pipes

 

[nvn]

About the twist, i don't think it's something to worry about ...

OK.

Next, you should also consider a horizontal load applied to the table top edge, such as a person pushing, or bumping, the table top edge, horizontally. Although I would not be able to show you the derivation due to time constraints, I can give you the formulas, as follows.

You could apply a horizontal load to the table top edge (pointing toward the table top center point) of V4 = 250 N. Therefore, the axial force applied to one vertical leg pipe, due to V4, will be P4 = -0.3340*V4*L2/x, where L2 = vertical leg pipe length, and x = leg pipe centerline spacing, as shown in your post 14 diagram. And the bending moment applied to the bottom or top of one vertical leg pipe, due to force V4, will be M4 = 0.1320*V4*L2. Add P4 to your previous P3, then compute the pipe uniform axial stress, sigma3. Compute the pipe bending stress due to M4. (An example of computing pipe bending stress was shown in post 13.) I.e., compute bending stress, sigma2 = M4*(0.5*D0)/I2. Then, compute the vertical leg pipe total stress, sigma4 = sigma3 - sigma2. Ensure stress level Rty4 = abs(sigma4)/Sta does not exceed 100 %, where Sta = 67.0 MPa.

 

[nvn]

Correction to the P1 formula I gave you in post 21:

Create a new variable, m2 = table top sector self mass = M_table*[theta0/(2*pi)]. Change P1 formula to, P1 = -(pi/theta0)[(m1 + m2)*g]/(4 legs).

Correction to post 50: Change D0 in post 50 to D_profile.

 

[dislect]

Thanks, i already included the self mass of a sector in P calculations