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Modélisation et simulation par éléments finis : examen

Exam 2010 « Finite element simulation »

Analysis of a grip for a cable extruder

Objectives and context:Overview

Closure Mechanism

Legend : alpha : angle of the cone = 10°P1s : force of the hydraulic system P1i : reaction force on the grip P2 : contact forceA1s : area corresponding to load P1s A1i : area corresponding to load P1iA2 : contact area between grip and external ring

The goal of this study is to analyse a grip of a cable extruder to check if it fits the design guidelines.

This grip is part of a cable co-extruder that is used to manufacture a cable and coat it with thermoplastics at the same time. At the beginning of the process, the grip is free of load (open state) and the end of the cable is inserted in the grip Then the grip is closed using a cone mechanism. Finally the cable is maintained in the grip and is pulled out of the co-extruder.

The closure mecanism of the grip os based on a cone and is activated by an hydraulic system that pulls back the outer ring until the desired contact pressure is reached

A finite element analysis is requested by the customer for the following reasons :

1) Checking that the design fullfills the basic requirement for normal « in operation » conditions (closure + cable + tension)

2) Checking the design in the case of maximum closure without cable (worst case scenario)

J. Cugnoni, LMAF/EPFL, 2010 p. 1 / 12


Geométry :

Load casesTwo load cases are considered in this study:

Load case no 1 :

In operation, we consider that a radial closure displacement dr=0.05mm is applied on surface A2. A contact pressure of 10 MPa exists then between the cable and the grips on surface A3. A nominal tension of the cable of 2000 N is considered (act on surface A3)

Analysis no 1 :

a) Simulate the load case 1

b) Verify that the maximal von Mises stress criteria is satisfied

Load case no 2 :

Secondly, we want to calculate the closure stiffness of the grip K1 = P1s / dr. The closure of the grip is modeled without the presence of the cable. The force P2 is calculated from P1s based on force equilibrium of the grip.The contact interface A2 is considered without friction and the outer ring is considered infinitelly rigid. The contact pressure p2= P2/A2 is considered constant over A2. The grip is rigidelly fixed to the external mechanism through a M6 screw.

Analysis no 2:

a) Calculate the contact pressure p2 = P2 / A2 from P1s

b) Simulate the load case no2 and calculate the stiffness K1=P1s/dr (considering the point pt2 for displacement)

c) Which force P1s should be applied to close the grip up to dr=0.1mm. Is the hydraulic system strong enough?

d) Using the linearity of the problem, verify that the von Mises stress criteria is verified for a closure displacement dr=0.1mm. What is the maximum hydraulic force P1s that can be applied before the grip fails?



e) Using the linearity of the problem, calculate the displacement at points pt1 (corner) and pt2 (middle of the edge) for P1s=1000 N

Design criteria:

The design criteria for the grip are :

1) Maximal von Mises stress < failure stress of the material / safety factor

2) Maximal force of the hydraulic system P1s = 1000N

3) Maximal closure of the grip dr = 0.1 mm

Material

High strength

Young’s modulus = 210 GPa

Poisson ratio= 0.3

Elasticity limit 0.2% = 800 MPa

Failure stress = 1200 MPa

Safety factor = 1.5

Density = 7850 kg/m3

Work and evaluation

To do your study, please follow the template here after.Once finished, the documents will be copied by the supervisor in electronic form.The following files must be transmitted: Word document (.doc), Abaqus model (.cae & .jnl) Just call the supervisor once finised to copy your exam files on his USB key.

The evaluation of the work is structured as follows :- Preparation of the model 20% - mesh convergence study 20%- Extraction of the results 20%- Analysis and conclusions 20%- Understanding of the problem, justification of the choices and overall quality of the report 20%

Duration expected: 3h (extension max 4h )

The CAD File can be downloaded sur http://lmafsrv1.epfl.ch/CoursEF2010/Examen2010/geom1.stp


http://lmafsrv1.epfl.ch/CoursEF2010/Examen2010/geom1.stp


Report

Analysis of a grip for a cable extruder

Exam 2010 « Finite element simulation » name, email adress, Sciper no

1.Objectives1.1 Objectives and context

Overview

Closure Mechanism

Legend : alpha : angle of the cone = 10°P1s : force of the hydraulic system P1i : reaction force on the grip P2 : contact forceA1s : area corresponding to load P1s A1i : area corresponding to load P1iA2 : contact area between grip and external ring

The goal of this study is to analyse a grip of a cable extruder to check if it fits the design guidelines.

This grip is part of a cable co-extruder that is used to manufacture a cable and coat it with thermoplastics at the same time. At the beginning of the process, the grip is free of load (open state) and the end of the cable is inserted in the grip Then the grip is closed using a cone mechanism. Finally the cable is maintained in the grip and is pulled out of the co-extruder.

The closure mecanism of the grip os based on a cone and is activated by an hydraulic system that pulls back the outer ring until the desired contact pressure is reached

A finite element analysis is requested by the customer for the following reasons :

3) Checking that the design fullfills the basic requirement for normal « in operation » conditions (closure + cable + tension)

4) Checking the design in the case of maximum closure without cable (worst case scenario)



Geometry :

Design criteria:

The design criteria for the grip are :

1) Maximal von Mises stress < failure stress of the material / safety factor

2) Maximal force of the hydraulic system P1s = 1000N

3) Maximal closure of the grip dr = 0.1 mm

1.2 Analysis type and methodology

!!!!!Which kind of analysis do you realize and why i !!!!

!!!!! What is the overall procedure that you will follow !!!!!

2. Geometric Hypotheses 2.1 Presentation of the geometry

This project involves only a single part : the grip to be modeled .

The geometry is given in a CAD file in STP format and is presented in the figure on page 4)

2.2 System of units

!!!!! which system of units to you use for this study !!!!

Length : unitéXXX

Force : unitéXXX

Mass : unitéXXX



Stress / module : unitéXXX

2.3 Characteristic dimensions

Characteristic dimensions of the part : length / diameter

2.4 Symmetries of the problem

!!!! Is there any symmetry in the problem ? which ones ? do you use them?

2.5 Geometry modeling space

!!!! Which kind of geometric model do you consider ?!!!

3. Physical behaviour hypothesis 3.1 Description of the materials

The grip is machined directly in a block of high strength steel

3.1.1 Constitutive model

!!!!! Which constitutive model do you consider to represent the material used here ?? !!!!!!

3.2 Constitutive Properties

The constitutive properties of the high strength steel used herein are as follows :

Young’s modulus XXX GPa

Poisson ratio XXX

Elasticity limit 0.2% XXX MPa

Failure stress XXX MPa

Safety factor xx

Density XXX kg/m3



3.3 Material property assignement

The part considered herein being homogeneous, the constitutive behaviour is applied to the whole part directly.

4. Loading Hypotheses 4.1 Boundary conditions model

1) Load case no 1In operation, we consider that a radial closure displacement dr=0.05mm is applied on surface A2. A contact pressure of 10 MPa exists then between the cable and the grips on surface A3. A nominal tension of the cable of 2000 N is considered (act on surface A3)

How do you model the load case no 1 in the FE simulation code :

!!!! which loads? How is it modelled? Which magnitude & direction ? !!!!

!!! Boundary condition: which type ? blocked degrees of freedom ? which coordinate system ? on which face ?

!!!!! 1 picture of the boundary conditions + load !!!!

IT IS STRONGLY ADVISED TO COMPLETELY FINISH THE LOAD CASE 1 BEFORE STARTING CASE 2

2) Load case no 2Secondly, we want to calculate the closure stiffness of the grip K1 = P1s / dr. The closure of the grip is modeled without the presence of the cable. The force P2 is calculated from P1s based on force equilibrium of the grip.The contact interface A2 is considered without friction and the outer ring is considered infinitelly rigid. The contact pressure p2= P2/A2 is considered constant over A2. The grip is rigidelly fixed to the external mechanism through a M6 screw.

How do you model the load case no 2 in the FE simulation code :

!!! calculation of the pression p2 from the force P1s

!!!! which loads? How is it modelled? Which magnitude & direction ? !!!!

!!! Boundary condition: which type ? blocked degrees of freedom ? which coordinate system ? on which face ?

!!!!! 1 picture of the boundary conditions + load !!!!



4.2 Symmetry conditions

!!!! If you use symmetries : which ones ? !!!!

4.3 Rigid body motions

!!!! If present how do you block them ? !!!!!!!

5. Discretization Hypotheses

Initial Mesh 5.1 Choice of the finite element type

ONLY CARRY OUT A CONVERGENCE STUDY FOR CASE 1 !!!!!! Which type of elements do you choose. Hex, Wedge, tet? Linear, quadratic? Mention

why …

!!!!!

5.2 Mesh generatin method, Size / nb elements

!!!!!!!! please present your choice of mesh generation method, meshing algorithm that you use and justify your choice briefly !!!!!!

Characteristic size of the mesh ? Nb of elements & nodes ?

=> picture of the inital mesh

Refined Mesh5.3 Choice of the finite element type

ONLY CARRY OUT A CONVERGENCE STUDY FOR CASE 1 !!!!!! Which type of elements do you choose. Hex, Wedge, tet? Linear, quadratic? Mention

why …

!!!!!

5.4 Méthode(s) de maillage, Taille / Nbre d'élémentsWhere should you refine the mesh and why ?



!!!!!!!! please present your choice of mesh generation method, meshing algorithm that you use and justify your choice briefly !!!!!!

Characteristic size of the mesh ? Nb of elements & nodes ?

=> picture of the refined mesh

6. Problem type and resolution6.1 Type of probem and solver options

!!!!! present briefly the problem and equation that you solve

6.2 Calculated results Linear statics analysis

The computed quantities in a linear statics problem are :the displacement field U, the stress tensor field and the strain tensor field

7. Etude de convergence de maillage7.1 Criteria

ONLY CARRY OUT A CONVERGENCE STUDY FOR CASE 1

Which result do you extract and compare to carry out the convergence study ? where are this results extracted ?

7.2 Initial mesh results

Representative values

Present hereafter the values that you compare to check convergence of the mesh

Comparison value Initial mesh Refined mesh

Nb de nodes xxx xxx

Quantity no1 XXXX!!!!!!!!!!!! xxx xxx

Quantity no2 XXXX !!!!!!!!!!!! xxx xxx

7.3 Estimation of the relative error and discussion on convergence & model accuracy

Compute the relative difference betwen the two meshes . is it acceptable ?



Which mesh will you use for the real analysis ?

Comment on the uncertainties of the results obtained with the chosen model

(even if it seems necessary don’t do a 3rd mesh refinement, just mention it if you think it would be worth doing ….)

8. Results8.1 Presentation of the results

a) Load case no 1

Field of von Mises equivalent stress

!!!1st Image (colormap) of the global mises stress distribution ;

!!!2nd Image (colormap) of the mises stress distribution close to the maxima

!!!What is the maximum von Mises stress value ?

Displacement field

!!!! Image (colormap) of the displacement field, where is the maximum and how much ? !!!!

b) Load case no 2

Field of von Mises equivalent stress


!!!1st Image (colormap) of the global mises stress distribution ;

!!!2nd Image (colormap) of the mises stress distribution close to the maxima

!!!What is the maximum von Mises stress value ?

Displacement field

!!!! Image (colormap) of the displacement field, where is the maximum and how much ? !!!!



Displacement vectors at pt 1 and pt 2

Point dx dy dz

Pt1 Xxx mm Xxx mm Xxx mm

Pt2 Xxx mm Xxx mm Xxx mm

9. Analysis & conclusions9.1 Criteria et analysis

a) Load case no 1Verify if the maximum von mises stress criteria is fullfilled or not ..

b) Cas de charge no 2


Calculate the stiffness K1=P1s/dr (consider the point pt 2 for displacement extraction )

Which force P1s should be applied to close the grip up to dr=0.1mm. Is the hydraulic system strong enough?

Using the linearity of the problem, verify that the von Mises stress criteria is verified for a closure displacement dr=0.1mm. What is the maximum hydraulic force P1s that can be applied before the grip fails?

Using the linearity of the problem, calculate the displacement at points pt1 (corner) and pt2 (middle of the edge) for P1s=1000 N

9.4 Conclusion:

Answer to the global question of the study.Does the part fullfills all the requirements ? What could be improved?

Name : XXXX

Date : XXXX



Email : XXXX


Documents

FEM - lmafsrv1.epfl.chlmafsrv1.epfl.ch/CoursEF2010/Examen2010/donnee1EN… · Web viewThe following files must be transmitted: Word document (.doc), Abaqus model (.cae & .jnl) Just