# Fabrication Layout Development of Eccentric Cone by using Geometric & Numerical Method with Example

In This Post we are going to explain how we can layout eccentric cone by using Geometrical or Graphical or Numerical Method with practical example for using this method.

Eccentric cone development mostly used in fabrication of kettle type re-boiler for easy removal of tube bundle from from the shell and this shape is also useful where bottom of the cone should be required as flat in fabrication of vessel.

So in this post we will discuss all the terms related to development of Eccentric cone lay outing on to the plates and cutting out the cutting profile of required size from the plate and Rolling of this blank plate on rolling machine or on point press and formed in to Desired shapes.

Whenever we use development calculation for any shapes it necessary to develop the layout using mean dimensions so that our required shape could be made in perfect size. If we are not use mean dimension in calculation of layout then it has variation in sizes after pressing.

## Geometrical or Graphical Method for Eccentric Cone Layout:

Steps for Geometrical Layout of Eccentric Cone:

1. Draw the Side view and half bottom view of the cone.

2. Divide the Base circle and top Circle in equal part as per our required accuracy.

3. Draw arc from point 2’, 3’, 4’, 5’, 6’, 7’ with centre of arc as 1’ as shown in figure.

4. Strike arc from the point 10,20,30,40,50,60,70 with centre as “O” as shown in above figure.

5. Measure the distance 1’– 2’, 2’-3’, 3’-4’, 4’-5’, 5’-6’, 6’-7’ with compass or divider and mark this distance on Arc drawn from point in step no4.

6. Fit the curve passing through point 1,2,3,4,5,6,7 etc and join all this point to make curve.

7. Repeat same procedure for top Diameter circle to obtain curve for top section.

by using this process we can get required dimension for lay-outing or we can use this method while lay-outing on Auto Cad.

## Numerical Method for Eccentric cone Layout:

Let,
D= Large Diameter or Bottom Diameter of Cone.
D1 = Small diameter or Top Diameter of Cone.
H = Overall Height of the Cone.
H1 = Straight Height of the cone.
C = Cord length of the cone.
S = Slant height of the cone.
N = No. of part to be divide the bottom or top Circle.

So,        tan α = ( D – D1 ) / H1 ;

H = D / tan α ; H2 = H – H1;

β = 360 / N ;

γ1 = β ; γ2 = 2*β ; γ3 = 3*β ; γ4 = 4*β ; γ5 = 5*β ; γ6 = 6*β ; γ7 = 7*β ——- so on.

Calculate C1, C2, C3, C4, C5, C6, and C7 …etc for bottom arcs.

C1 = D * sin ( γ1 / 2 ) ; C2 = D * sin ( γ2 / 2 ) ; C3 = D * sin ( γ3 / 2 ) ; C4 = D * sin ( γ4 / 2 ) ;

C5= D * sin ( γ5 / 2 ) ;

Slant arc length S1, S2, S3, S4, S5, S6,…. etc. for bottom arcs.

S1 = √(H2 + C12); S2 = √(H2 + C22); S3 = √(H2 + C32); S4 = √(H2 + C42); S5 = √(H2 + C52); S6 =√(H2 + D2);

Calculate C1*, C2*, C3*, C4*, C5*, C6*, etc for top arcs.

C1* = D1 * sin ( γ1 / 2 ) ; C2* = D1 * sin ( γ2 / 2 ) ; C3* = D1 * sin ( γ3 / 2 )

; C4* = D1 * sin ( γ4 / 2 ) ; C5*= D1 * sin ( γ5 / 2 ) ;

Slant arc length S1*, S2*, S3*, S4*, S5*, S6* etc. for top arcs.

S1* = √(H22 + C12); S2* = √(H22 + C22); S3* = √(H22 + C32); S4* = √(H22 + C42); S5* = √(H22 + C52);

S6 *=√(H22 + D2);

Mark all the dimensions for lay outing eccentric cone and cut out profile from the plate.

from all the above calculated values we can layout eccentric Cone.

And Finally we want share link of our Android Application for calculating Eccentric cone layout by numerical method in faster way. we had made this tool for use of this concept in your mobile for minimize your daily fabrication work.

Example of Eccentric Cone Layout using this Method:

Develop the layout of eccentric cone having bottom diameter 500 mm and top diameter 300 mm having straight height is 400 mm.

tan α = ( D – D1 ) / H1 = ( 500 – 300 ) / 400 = 0.5 ;

H = D / tan α = 500 / 0.5 = 1000 mm ; H2 = H- H1 = 1000-400 = 600 mm

β = 360 / N = 360/12 = 30 degree;

γ1 = β ; γ2 = 2*β ; γ3 = 3*β ; γ4 = 4*β ; γ5 = 5*β ; γ6 = 6*β ; γ7 = 7*β ——- so on.

Calculate C1, C2, C3, C4, C5, C6, and C7 for bottom arcs.

C1 = D*Sin( γ1 / 2 ) = 500*sin(30/2)=129.4 mm;
C2 = D * sin (γ2 / 2) = 500 * sin (2*30/2) =250 mm;
C3 = D * sin (γ3 / 2) = 500 * sin (3*30 / 2) = 353.55 mm;
C4 = D * sin ( γ4 / 2 ) = 500 * sin (4*30/2) = 433.01 mm;
C5= D * sin ( γ5 / 2 ) = 500 * sin (5*30 / 2 ) = 482.96 mm;

Slant arc length S1, S2, S3, S4, S5, S6 for bottom arcs.

S1 = √(H2 + C12) = √(10002 + 129.42) = 1008.33 mm;
S2 = √(H2 + C22) = √(10002 + 2502) = 1030.77 mm;
S3 = √(H2 + C32) = √(10002 + 353.552) = 1060.65 mm;
S4 = √(H2 + C42) = √(10002 + 433.12) = 1089.7 mm;
S5 = √(H2 + C52) = √(10002 +482.962) = 1110.05 mm;
S6 = √(H2 + D2) = √(10002 + 5002) = 1118.03 mm;

Calculate C1*, C2*, C3*, C4*, C5*, C6*, and C7* for Top arcs.

C1* = D1*Sin( γ1 / 2 ) = 300*sin(30/2)=77.64 mm;
C2* = D1 * sin (γ2 / 2) = 300 * sin (2*30/2) =150 mm;
C3* = D1 * sin (γ3 / 2) = 300 * sin (3*30 / 2) = 212.13 mm;
C4* = D1 * sin ( γ4 / 2 ) = 300 * sin (4*30/2) = 259.8 mm;
C5*= D1 * sin ( γ5 / 2 ) = 300 * sin (5*30 / 2 ) = 289.7 mm;

Slant arc length S1*, S2*, S3*, S4*, S5*, S6* for Top arcs.

S1* = √(H22 + C1*2) = √(6002 + 77.642) = 605 mm;
S2* = √(H22 + C2*2) = √(6002 + 1502) = 618.4 mm;
S3* = √(H22 + C3*2) = √(6002 + 212.132) = 636.3 mm;
S4* = √(H22 + C4*2) = √(6002 + 259.82) = 653.8 mm;
S5* = √(H22 + C5*2) = √(6002 +289.72) = 666.27 mm;
S6* = √(H22 + D12) = √(6002 + 3002) = 670.8 mm;

2-2= S1 – S1* = 1008.33 – 605 = 403.3;

3-3’= S2 – S2* = 1030.77 – 618.4 = 412.3;

4-4’= S3 – S3* = 1060.55 – 636.3 = 424.0;

5-5’= S4 – S4* = 1089.7 – 653.8 = 435.9;

6-6’= S5 – S5* = 1110.03– 666.27= 444.2;

7-7’= S6 – S6* = 1118.03 – 670.8 = 447.2;

and using all this values we can layout Eccentric cone by Numerical method it is advisable to use our app for this calculation and faster layout development with accuracy. this method is explaining to know mathematics behind lay-outing methods of Eccentric Cone.

please share this post and application for those who are in field of fabrication and also give your suggestion making new tools ease of fabrication methods.