 Open Access
 Total Downloads : 4
 Authors : D.R. Joshua, J.Kadhir Selvan
 Paper ID : IJERTCONV3IS16126
 Volume & Issue : TITCON – 2015 (Volume 3 – Issue 16)
 Published (First Online): 30072018
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Design of Round to LSction using BSpline Curve
D.R. Joshua,
Assistant Professor, AVS Engineering College, Salem.
J.Kadhir Selvan,
Associate Professor, AVS Engineering College, Salem.
Abstract: In recent days there has been a growing need in the manufacturing industry to supply the needs of the globe. In manufacturing process like cutting, drilling, shaping etc., there is high material wastage and less dimensional accuracy. Moreover complex shapes cannot be obtained easily. Metal forming by extrusion, one of the widely used metals forming process can be a suitable solution to solve these problems. In bulk production extrusion plays a major role in saving the time and makes the process easier and simpler.
In extrusion process, extrusion die plays a major role. The die has a require profile through which the component is extruded. By using stream lines we are able to obtain the profile. But by using stream lines we cant get closeness of the curve, so we are using Bspline curve, a geometrical curve to overcome this problem. The main advantage of this curve is it can be adjusted any point to get the required profile.
In our research, we designed the extrusion die profile using Solid Works and analyzed it with DEFORM3D software for the extrusion of Lsection using Bspline curves. Since Lsection has numerous engineering applications and it can be bear high compressive load.

INTRODUCION

EXTRUSION
Extrusion is a process used to create objects of a fixed crosssectional profile. A material is pushed or drawn through a die of the decided crosssection. The two main advantages of this process over other manufacturing processes are its ability to create very complex cross sections and work materials that are brittle, because the material only encounters compressive and shear stresses . It also forms finished parts with excellent surface finish.
Extrusion may be continuous (theoretically producing indefinitely long material) or semicontinuous (producing many pieces). The extrusion process can be done with the material hot or cold. Commonly extruded materials include metals, polymers, ceramics, concrete and food stuffs.
Fig 1.0 Extrusion

ADVANTAGES OF EXTRUSION

Uniform crosssectional area over a long length.

Low cost of dies making it economical to make small quantities of a shape.

Good surface finish


TYPES OF EXTRUSION

Cold Extrusion.

Hot Extrusion

Direct Extrusion

Indirect Extrusion

Hydrostatic Extrusion


COLD EXTRUSION.
Cold Extrusion is done at room temperature or near room temperature. The advantages of this over a hot extrusion are the lack of oxidation, higher strength due to cold working, closer tolerances, good surface finish, and fast extrusion speeds if the material is subject to hot shortness. Materials: lead, Tin, Aluminum, Copper, zirconium, Titanium, Molybdenum, Beryllium, Vanadium, Niobium and steel.
Examples: Collapsible tubes, Extinguisher cases, shock absorber cylinders and Gear blanks

HOT EXTRUSION
Warm extrusion is done above room temperature, but below the recrystallization temperature of the material the temperature ranges from 800 to 1800 oF (424 to 975 oC). It is usually used to achieve the proper balance of required forces, ductility and final extrusion properties.

DIRECT EXTRUSION
Direct extrusion is also known as forward extrusion, is the most common extrusion process. It works by placing the billet in a heavy walled container. The billet is push through the die by a ram or screw. There is a reusable dummy block between the ram and the billet to keep them separated. The major disadvantage of this process is that the force required to extrude the billet is greater than the need in the indirect extrusion process because of the frictional forces introduce by the need for the billet to travel the entire length of the container.
Fig 1.1Direct Extrusion

INDIRECT EXTRUSION
In indirect extrusion also known as backwards extrusion, the billet and container move together while the die is stationary. The die is held in place by a stem which has to be longer than the container length. The maximum length of the extrusion is ultimately dictated by the column strength of the stem. Because the billet moves with the container the frictional forces are eliminated.
Fig 1.2 Indirect Extrusion

HYDROSTATIC EXTRUSION
In the hydrostatic extrusion process the billet is completely surrounded by a pressurized liquid, except where the billet contacts the die. This process can be done hot, warm,
cold, however the temperature is limited by the stability of the fluid used. The process must be carried out in a sealed cylinder to contain the hydrostatic medium.
Fig 1.3 Hydrostatic Extrusion


PROBLEM IDENTIFICATION
Fig 2.1 Designing of extrusion die for converting circular to L Section using BSpline curves

CONSIDERATION IN DIE DESIGN

Desired shape of the product

Material

Billet size

Number of die cavities

Process tool

Extrusion temperature

Extrusion pressure

Die material

For converting circular section to Lsection, the profile should be modified using Bspline curves. We have to find what will be the length of the die. We have to compress most of the material over here because it is easy to extruding a square from circle is simple there they are compressing some low amount of material. But here in Lsection we are compressing large amount of material so we have to apply high pressure and large amount of stress is created over the surface of die.


SCOPE OF THE PROJECT
Ni,1(t) =
4.2 KNOT VECTORS
1 ti t < ti+1
0 Otherwise
Fig 3.1 LSection Beam
L Section, giving many benefits. It is very good for giving stiffness (less deformation on loading) and to withstand higher bending moments (as a result of heavy loading) and to with other crosssectional shapes of same area. Also, it is very easy to manufacture.

It is very good for giving stiffness (less deformation on loading) and to withstand higher bending moments (as a result of heavy loading) on compression with other cross sectional shapes of same area.

Also, it is very easy to manufacture.

LAngle flange provides more load distribution contact area at key loading points.

LAngle flange provides the greatest deck support by increasing deck thickness at impact points

Spacing between beams is kept to minimum and increase the rigidity of the deck.

LAngle has the least twisting action when loaded with sheer force.


INTRODUCTION TO BSPLINE CURVES.

Definition of the BSpline Curve.
A Bspline curve P(t), is defined by Where,

the {Pi : i = 0, 1, …, n} are the control points

k is the order of the polynomial segments of the B spline curve. Order k means that the curve is made up of piecewise polynomial segments of degree k

1,

The Ni, k(t) are the normalized Bspline blending functions. They are described by the order k and by a nondecreasing sequence of real numbers
{ti :i = 0, .., n + k} .
normally called the knot sequence. The Ni,k functions are described as follows :
A knot vector is a list of parameter values, or knots, that specify the parameter intervals for the individual BÂ´ezier curves that make up a Bspline. For example, if a cubic B spline is comprised of four BÂ´ezier curves with parameter intervals [1, 2], [2, 4], [4, 5], and [5, 8], the knot vector would
be [t0,t1, 1, 2, 4, 5, 8, t7, t8].Notice that there are two (one less than the degree) extra knots prepended and appended to the knot vector. These knots control the end conditions of the B spline curve, For historical reasons, knot vectors are traditionally described as requiring n endcondition knots, and in the real world you will always find a meaningless additional knot at the beginning and end of a knot vector.
Fig 4.1 knot vector.

MULTIPLE KNOTS
If a knot vector contains two identical nonend condition knots ti = ti+1, the Bspline can be thought of as containing a zerolength BÂ´ezier curve over [ti, ti+1]. Figure 8 shows what happens when two knots are moved together. The BÂ´ezier curve over the degenerate interval [5, 5] has polar values P(5, 5, 5), P(5, 5, 5), P(5, 5, 5),P(5, 5, 5), which is
merely the single point P(5, 5, 5).
Fig. 4.2 Multiple knots

PROPERTIES OF BSPLINE SURFACES

The highest order in each parametric direction is limited to the number of defining polygon vertices in that direction

The continuity of the surface in each parametric direction is k2, l2 respectively

The surface is invariant to an affine transformation

The variation diminishing property of Bspline surface is not well known

The influence of any polygon net vertex is limited to k/2, l/2 spans in the respective parametric direction.

If the number of polygon net vertices is equal to the order of basis in that direction and if there are no interior knot values, then the Bspline surface reduces to a Bezier surface.

The flexibility of Bspline curves and surfaces is increased by raising the order of the basis function and hence the defining polygon/grid segments.

The nature of the knot vector is preserved (uniform, open) even after insertion of new knot value


ADVANTAGES OF USING BSPLINE
CURVES

Bspline curve require more information (i.e., the degree of the curve and a knot vector) and a more complex theory than Bezier curves.

But it has more advantages to offset this short coming

First, a Bspline curve can be a Bezier curve.

Second, Bspline curve satisfies all important properties that a Bezier curve has.

Third, Bspline curve provide more control flexibility than Bezier curve can do.


DESIGNING OF DIE FOR LSECTION IN SOLID WORKS SOFTWARE

DESIGN OF EXTRUSION DIE USING B SPLINE CURVES.
Here we are using BSpline curves for designing the extrusion die to convert a round billet to an LSection beam. The design process is as follows.
Fig 5.1The Solid Works interface.
Initially the L section is drawn in the front plane with the basic dimensions
Fig 5.2 LSection in front plane.
Create one offset plane at a distance of 10 mm from the front plane and draw a circle of diameter 30 mm. select 3D sketch from tool bar and join the circle with the L section using 5 splines
If we join the two sections without guide curves, it will be a streamlined die. To apply our concept in this die we should connect the two sections with the BSpline curves. We took the guide curves from each corners of the LSection and connected to the circular section. Totally we take 5 Guide curves to join the two sections.
The following fig shows the process of creating the BSpline curves for connecting two sections.
fig 5.3 complete diagram which is connected by 5spline curves.
Now the sketching part is over. Then by using LOFTED SURFACE command the sketch is converted into the part. When using the LOFTED SIRFACE command the two sections are selected in the profile area and the guide curves are selected in the guide area.
Fig 5.4 Using LOFTED SURFACE command
Thus a die with a sheet metal thickness is produced. We can add the thickness up to the required level by using THICKEN option.
INSERT BOSS/BASE THICKEN
Thus the die profile is created. But practically it is not possible to extend an Object without using guide ways. So we should create an guide path for the work piece to enter into the die profile. It is created by using EXTRUDED BOSS/BASE command by leaving the hollow space in the centre to permit the work piece.
Fig 5.5 Final die using B spline curves.
Thus the die is well prepared using B spline curves and it is shown in the following figures
Front view.
Top view.
Isometric view.
Fig 5.6 Die using B spline curves

DESIGNING OF EXTRUSION DIE USING NORMAL STREAMLINED CURVES
Streamlined dies are the commonly used dies in the market. To compare our newly designed die using Bspline curves we need to design the streamlined die for the same section and same dimensions.
The same procedure as like above is followed for this process. But instead of creating spline curves for the guide curves we use straight lines. Remaining all the commands are same.
Fig 5.7 complete diagram which is connected by straight lines.
Fig 5.8Use of streamlined guide curves
Fig 5.9 Final die using streamlined curves.
Thus the die is well prepared using Straight line curves and it is shown in the following
Front view
Top view
Isometric view
Fig 5.10 Die using Straight line curves

DESIGNING OF TOP DIE (RAM)
Top die is nothing but the ram, Which is used to push the work piece through the die or to give load to the work piece for extrusion. It is a cylindrical object with circular cross section. Designing of top die (ram) is a simple process which requires sketching the circle using Circle command and the
solid cylinder is made Using EXTRUDED BASE.
Fig 5.11 Designing of Top die

DESIGNING OF WORKPIECE (BILLET)
Work piece is nothing but a billet. Here the work piece has a cylindrical cross Section of diameter 30mm with some tolerance.
Designing of work piece is same as the top die by using solid works, In this project we are going to convert a circular billet to LSection.
Work piece is heated up to recrystallisation temperature and then it is passed into the die profile and required Lsection is extruded.
5.12 Designing of Work piece


ANALYSIS USING DEFORM 3D SOFTWARE

ANALYSIS OF EXTRUSION PROCESS THROUGH DIEDESIGNED USING B SPLINE CURVES.
Then the main screen opens. The interface screen is shown below :
Fig 6.1 Main Screen
The various steps have to be followed is as follows:

Simulation Control Settings
In this step the units, Type of problem, Number of steps to be simulated and Top die displacements are fed here.
Fig 6.2 Simulation Cntrols

Loading Object Data

This process comprises of importing the needed objects i.e., Work piece, Bottom die, Top die into the working area.
Initially the work piece have to be imported and it is meshed in to several small objects.
Fig 6.3 Meshed Work piece.
Then the properties of the material for the work piece is selected and also the temperature for the work piece is specified.
Fig 6.4 Specifying Work piece Properties
Then the top and bottom die is inserted and they are aligned properly in the manner so that their axis should lie in straight line.
Fig .6.4 Object Positioning
And then the material properties for both the dies are specified
Fig 6.4 specifying die propertiesThen the relevant steps are given to the Top Die to push the Work piece through the Bottom Die with the appropriate increment steps.
The next step is to run the SIMULATION. Here the deformation is being carried out step by step.
The next step is DEFORM POST PROCESSOR. In post processor, the exact results of both the Bspline and Streamline dies are obtained.
7. RESULTS.

EXTRUSION DIE USING BSPLINE CURVES.
Fig 7.1 Output of Lsection (BSpline Die)
Velocity in Bspline die.
Fig. 7.2 velocity in bspline dies.
Stress in BSpline Die
Fig 7.3 Stress in Bspline
Load Prediction in Bspline Die
Fig 7.2 Load Prediction in BSpline Die
Damage in bspline die.
Fig 7.3 Damage in bspline die.

EXTRUSION DIE USING STRAIGHT LINE CURVES.
Fig 7.4 Output of Lsection (Streamline)
Velocity in Streamline Die.
Fig 7.5 velocity in Streamline Die.
Stressin Streamline Die.
Fig 7.6Stress in Streamlined Die.
Load Prediction in Streamline Die
Fig 7.7 Load Prediction in streamline Die
Damagein Streamline Die.
Fig 7.8Damege in Streamlined Die.
8.7. CONCLUSION.
The purpose of our project is to design the extrusion die for converting circular billet to L section by using BSpline curves. The designing part is done using SolidWorks software and the analysis part is done using Deform 3D software.
The analysis part is done for both the dies, i.e., Bspline die and Streamline die , and the results are compared. When we compare the results, the following statistics are found.

The velocity of ram movement is increased up to (2.8mm/sec) in Bspline die than in Streamline die.

Stress in the workpiece is low when compared to other dies up to 240 Mpa

Load required for the extrusion process has been reduced upto 230 KN

Damage in the workpiece extruded through the Bspline die is less (3.05) than the Streamlined Die (3.45)

9. REFERENCES.

Juan Cao, Guozhao Wang, Institute of Image Processing and Computer Graphic, Department of Mathematics, Zhejiang University, Hangzhou, China, The structure of uniform Bspline curves with parameters 29 September 2007.

FUHUA CHENG, University of Kentucky, Lexington, U.S.A.
,XUEFU WANG SoftImage, Montreal, Quebec, Canada, B. A. BARSKY, University of California, Berkeley, U.S.A. , Quadratic B
Spline Curve Interpolation, April 2000

L.H. You , J.H. Hu, Y.H. Shi , J.J. Zhang , National Centre for Computer Animation, Bournemouth University, Talbot Campus, Ac Kenneth Grubb Associates Ltd., Bournemouth , UK Singlepatch surfaces for tool shape design and finite element analysis of hot extrusion , April 2004

Thomas W. Sederberg, An Introduction to BSpline Curves , March 14, 2005

Kenneth I. Joy, Visualization and Graphics Research Group, Department of Computer Science, University of California, Davis. Definition of a bspline curve , The uniform bspline blending functions , November 2000.

K.J. Maccallum , J.M. Zhang, Faculty of Engineering CAD Centre,
University of Strathclyde, Glasgow, China, Curvesmoothing Techniques Using
Bsplines , July 2003.

S.K.Sahoo, P.K.Kar, K.C.Singh, Department of Mechanical Engineering, Indira Gandhi Institute of Technology, Sarang,
Dhenkanal, A Numerical application of the upperbound technique for roundtohexagon extrusion through linearly converging dies. , 22 December 1997.

Kirubel Bogale, Simulation and Design of Extrusion Dies Plastics Technology 2011.

R. Narayanasamy, R. Ponalagusamy, R. Venkatesan, P. Srinivasan, Department of Production Engineering, NIT, Trichy, Tamilnadu, India An upper bound solution to extrusion of circular billet to circular shape through cosine dies,16 November 2005

MiklÂ´os Hoffmann and Imre JuhÂ´asz, Institute of Mathematics and Computer Science, KÂ´aroly EszterhÂ´azy College, Hungary, On Interpolation by Spline Curves with Shape Parameters ,July 2008.

YU Chenglong and LI Xiaoqiang, School of Mechanical Engineering
and Automation, Beihang University,China Theoretical analysis on springback of
Lsection extrusion in rotary stretch bending process , 4 March 2011.

Milivoje M. Kostic and Louis G. Reifschneider, Department of Mechanical Engineering, Northern Illinois University U.S.A., Design of Extrusion Dies , july 2006.

Y. E. Beygelzimer and V. A. Beloshenko, Donetsk Physics and Technology, Ukraine SolidState Extrusion , July 15, 2004.