radieÖvergÅngsoptimering pÅ slagkolv634173/fulltext01.pdf · hyperworks, hypermesh, hyperview,...

Örebro universitet Örebro University Institutionen för naturvetenskap och teknik School of Science and Technology 701 82 Örebro SE-701 82 Örebro, Sweden

Examensarbete 15 högskolepoäng C-nivå

RADIEÖVERGÅNGSOPTIMERING PÅ

SLAGKOLV

Henrik Gustafsson och Emil Tjus

Maskiningenjörsprogrammet 180 högskolepoäng

Örebro vårterminen 2013

Examinator: Johan Kjellander

[FILLET OPTIMIZATION ON IMPACT PISTON]

Örebro University 3 June 2013 2 (42)

Abstract: At Örebro University, a part of the Bachelor of Science in Mechanical Engineering, a degree

project of 15 credits is to be made at the end of the education. This project can be

performed at the university or at a company, and the purpose is to prepare the student for

the upcoming employment after examination. This degree project were performed by Emil

Tjus and Henrik Gustafsson during the spring of 2013 at Atlas Copco Rock Drills AB in Örebro

on the department of Applied Mechanics.

The subject of this project was to configure and execute an optimization of a fillet on an

impact piston from Atlas Copco Rock Drills AB. The reason to optimize the fillet were founded

in the wish to increase the fatigue lifetime of the impact piston.

The optimization was performed in HyperWorks 12.0, a software that the department of

Applied Mechanics not normally uses. This caused finite element models from previous work

to be converted and evaluated to ensure that the models were correct configured in

HyperWorks.

The steps that was taken in HyperWorks towards an optimization were done by setting up an

approach called Design Of Experience. The results were then evaluated in the next step, an

approach called Fit. After this step, an approach called Optimization were run to generate

specific design parameters with the lowest possible stress range of the model. These

parameters were then applied to a finite element model and an analysis was made to verify

the result from the optimization.

The results of the optimization lowered the total stress range in a fictitious impact piston

from 1146,1 MPa to 717,4 MPa. This result was to be compared with the reference value of

604,7 MPa and the reference impact piston had a simple radial fillet. The result of this

project did not yield any improvements of the impact piston. However, an optimization of

the fillet was configured and completed in HyperWorks and this can hopefully be at use in

future analysis.


Sammanfattning: Vid Örebro universitet, en del av högskoleingenjörsexamen i maskinteknik, skall ett

examensarbete om 15 hp göras i slutet av utbildningen. Detta projekt kan utföras vid

universitetet eller på ett företag och syftet är att förbereda studenten för kommande

arbetsliv. Detta examensarbete utfördes av Emil Tjus och Henrik Gustafsson under våren

2013 på Atlas Copco Rock Drills AB i Örebro på avdelningen Applied Mechanics.

Ämnet för detta projekt var att konfigurera och genomföra en optimering av en

radieövergång på en slagkolv från Atlas Copco Rock Drills AB. Orsaken till optimeringen av

radieövergången är en önskan att öka utmattningslivslängden på slagkolven.

Optimeringen utfördes i HyperWorks 12.0, en programvara som avdelningen Applied

Mechanics normalt inte använder. Finita element modeller från tidigare arbeten behövde

därför konverteras och utvärderas för att säkerställa att modellerna var korrekt konfigurerade

i HyperWorks.

De moment som vidtagits i HyperWorks mot en optimering utfördes genom ett steg kallat

Design Of Experience. Detta steg korskör 3 geometrier med 5 olika värden i totalt 125 olika

analyssteg. Resultaten utvärderades i nästa steg som kallas Fit. Vidare startades

optimeringsalgoritmen vilket genererade specifika värden på de designvariabler som

resulterade i en geometri med lägsta möjliga spänningsomfång. Dessa värden applicerades

sedan på en finita element modell och gjordes en analys för att verifiera resultatet från

optimeringen.

Resultatet av optimeringen sänkte den totala spänningsvidden i en fiktiv slagkolv från 1146,1

MPa till 717,4 MPa. Resultatet jämfördes med referensvärdet på 604,7 MPa och

referenskolven hade en enkel radieövergång. Resultatet av detta projekt gav inte några

förbättringar av slagkolven jämfört med referensvärdet. Emellertid konfigurerades och

genomfördes en optimering av radieövergången i HyperWorks vilket kan ses som en

möjlighet för framtida analyser.


Table of Contents Abstract: ..................................................................................................................................... 2

Sammanfattning: ........................................................................................................................ 3

Table of Contents ........................................................................................................................ 4

1 Acknowledgements ............................................................................................................ 6

2 Abbreviations ..................................................................................................................... 7

3 Background ......................................................................................................................... 8

3.1 Rock Drills .................................................................................................................... 8

3.2 Rocktec Division ........................................................................................................... 9

3.3 Previous work .............................................................................................................. 9

3.4 Geometry ..................................................................................................................... 9

3.5 Software differences .................................................................................................... 9

3.6 Software ....................................................................................................................... 9

3.7 Hardware ..................................................................................................................... 9

3.8 Explicit ........................................................................................................................ 10

3.9 Optimization modules ............................................................................................... 10

3.10 Limitations of optimization ........................................................................................ 10

4 FE Model ........................................................................................................................... 11

4.1 Mesh .......................................................................................................................... 11

4.1.1 Previous mesh .................................................................................................... 11

4.1.2 Thesis mesh ........................................................................................................ 11

4.1.2.1 Analysis of mesh ......................................................................................... 12

4.1.2.2 Results of mesh analysis ............................................................................. 13

4.1.3 Analysis of spin ................................................................................................... 16

4.1.3.1 Result of spin analysis ................................................................................. 16

4.2 Initial Conditions ........................................................................................................ 18

4.3 Components .............................................................................................................. 19

4.4 Material ..................................................................................................................... 19

4.5 Constraints ................................................................................................................. 20

4.5.1 EngineFile ........................................................................................................... 20

4.6 Property ..................................................................................................................... 20

4.7 Contact ....................................................................................................................... 20

4.7.1 Detach or translate ............................................................................................. 21


4.8 Damping ..................................................................................................................... 22

4.9 Results of model setup .............................................................................................. 22

5 Calculation ........................................................................................................................ 23

5.1 Tresca ......................................................................................................................... 23

6 Optimization ..................................................................................................................... 24

6.1 Model ......................................................................................................................... 24

6.2 2D-Shell ...................................................................................................................... 24

6.3 Morphing ................................................................................................................... 25

6.4 Fourier curves ............................................................................................................ 25

6.5 Shapes ........................................................................................................................ 26

6.6 Approach of optimization .......................................................................................... 28

6.6.1 DOE - Fit - Optimization ...................................................................................... 29

6.6.1.1 Response Script ........................................................................................... 30

6.6.1.2 Full Factorial ................................................................................................ 31

6.6.2 Fit ........................................................................................................................ 31

6.6.2.1 Moving least squares .................................................................................. 31

6.6.3 Optimization ....................................................................................................... 32

6.6.3.1 Genetic algorithm ....................................................................................... 32

7 Result of Optimization ...................................................................................................... 33

8 Discussion ......................................................................................................................... 35

9 Reference .......................................................................................................................... 36

10 Appendix........................................................................................................................... 37

10.1 Previous Mesh ........................................................................................................... 37

10.2 Previous results .......................................................................................................... 37

10.3 Software specifics ...................................................................................................... 38


1 Acknowledgements

We will like to dedicate a special thanks to our tutor Robert Pettersson,

Specialist – Mechanical Analysis at Atlas Copco, Rocktec Division, Applied mechanics for all

technical support and guidance throughout the thesis.

Erik Magnemark, Application Engineer at Altair Engineering AB for all his technical support in

HyperWorks, HyperMesh, HyperView, HyperMath, OptiStruct and HyperStudy.

Karin Kraft, our tutor and lecturer at the Department of Science and Technology at Örebro

University for her inspiring speeches that have helped us through the thesis in hard times.

The former Atlas Copco, Rocktec Division, Applied Mechanics Specialist Manager

Jonas Larsson for the opportunity to do this thesis at Atlas Copco.

The whole Atlas Copco, Rocktec division for the engaged involvement throughout the thesis.

Last but not least, our families for the support they have given us throughout this thesis.

Thank you all!

Henrik Gustafsson

Emil Tjus

Örebro University

2013


2 Abbreviations

A_Steel Atlas Copco Steel for pistons

ACD Atlas Copco drill

ACP Atlas Copco piston

ACRD Atlas Copco Rock Drills AB

ANSYS Simulation and analysis program ANSYS APDL

version 14.0

APDL ANSYS Parametric Design Language, A.K.A ANSYS

Classic

CAD Computer Aided Design

CMT Construction and Mining Technique

DOE Design of Experience

FE Model Finite Element Model

GA Genetic Algorithm

HHT method Numerical damping in ANSYS version 14.0

HyperMath Numerical computing software

HyperMesh Pre-analysis software

HyperMorph Morphing tool in HyperMesh

HyperStudy Optimization software

HyperView Post-analysis software

HyperWorks Program used for pre-/ post-analysis and

optimization.

Matlab Program used for running mathematical and

technical calculations

MLSM Moving least square method

R&D Research and Development

Radioss The solver used by HyperWorks for solving non-

linear problems under dynamic loads

Rho_Initial Density in HyperWorks

VIS_F Critical damping coefficient on interface friction

VIS_S Critical damping coefficient on interface stiffness


3 Background

3.1 Rock Drills ACRD is one of the leading developers in rock drill technology and extensive R&D is made on

site in Örebro, Sweden. ACRD holds a large volume of the market shares [1]. Atlas Copco

manufactures rock excavating machines and applied on these machines different types of

rock drill equipment are mounted. The rock drill shown in figure 1 uses hydraulics to

generate shockwaves that travel through drill rods and generates a force to the rock, which

then brakes. The shockwave were generated by having an impact piston, shown in dashed

ellipse in figure 1. Inside the rock drill the impact piston works at high speed and frequency

striking the drill rod. The speed, frequency and weight of the piston generated high amounts

of kinetic energy. The energy is transferred to the drill rod and generated shockwaves that

braked the rock. The impact piston suffered from fatigue failure at the impact pistons tail due

to though work. Studies at ACRD, Rocktec Division, Applied Mechanics have confirmed that

the fatigue failure occurs in the impact piston where the stress range between compression

and tensile are greatest [2] [3]. Previous work have been executed to generate an optimum

transfer at the fillet of interest. The figure 2 shows the complete setup from previous work

and this geometry is used throughout this thesis.

Figure 1: Rock drill model from ACRD.

Figure 2: The complete setup figure from previous work at ACRD, Rocktec Division, Applied Mechanics.

Fillet of interest


3.2 Rocktec Division The department of the thesis work was Applied Mechanics at ACRD in Örebro. The

department is a group of specialized engineers that have their focus of expertise in CMT. The

team of engineers handles problems involving Solid Mechanics, Structural Strength, Fatigue,

Shock Vibrations, Optimization, Applied Statics, Numerical Simulations and Laboratory

Testing. Programs used within the department were ANSYS, ADAMS, AutoCAD, HyperWorks,

Matlab, HOPSAN, Math CAD, ProEngineer, WINFLAG and similar analytical programs.

3.3 Previous work Durability of the impact piston is insufficient due to fatigue. The impact piston works in the

range of 50-100 Hz at 4-40 kW. The weakness in the piston is the radius on the tail where

notches occur. Previous work have already been made on this by the applied mechanics

group. This was an evaluation of the possibility to generate values similar to that work in an

explicit analysis with a 3D model in HyperWorks. The programs used in the previous work

were ANSYS version 14 and Matlab version 7.9.0. The aim for this thesis will first of all

regenerate the results from the earlier work in HyperWorks version 12.0 and then make an

optimization of the fillets topology.

3.4 Geometry The geometry will be taken from the previous work material so that the evaluation will

be as accurate as possible. The thesis will contain two geometries, the drill rod and shank

adapter together and the impact piston. These geometries were imported to HyperWorks

from ANSYS APDL. This thesis will import the 2D geometry from ANSYS APDL and spun it into

a 3D model in HyperMesh.

3.5 Software differences This thesis will try to mimic the FE Model made in ANSYS APDL, and converted to

HyperWorks. Differences under the process will be dealt with individual.

3.6 Software The software in the thesis was HyperWorks version 12.0 from Altair Engineering. HyperWorks

consists of different modules used for pre-/ post-analysis and optimization. HyperMesh, used

for pre-analysis, HyperView, used for post-analysis, HyperStudy, used for optimization and

HyperMath, used for numerical computing analysis will be used in the thesis. Microsoft

Office 2013 was used for all types of documentation.

3.7 Hardware The processor in the computer that were used in the thesis were two 6-cored CPU: s with

48.0 GB RAM each at 3,47GHz. In the calculations only ten of the twelve cores were used due

to software license limitations.


3.8 Explicit The HyperWorks solver Radioss works in two formats, block and bulk. Bulk is for implicit and

block for explicit. The accuracy of the results by the explicit method is better than the implicit

method [4].The problem was of explicit characteristic due to the response time 300 µs and

block format were therefore chosen. In table 1 and 2 an evaluation was made when implicit

or explicit solution was required [5].

Solution Impact Velocity

(m/s) Strain Rate

(/s) Effect

Implicit < 10-5 Static / Creep

< 50 10-5 - 10-1 Elastic

50 - 1000 10-1 - 101 Elastic-Plastic (material strength significant)

1000 - 3000 105 - 106

Primarily Plastic (pressure equals or exceeds material strength)

3000 - 12000 106 - 108 Hydrodynamic (pressure many times material strength)

Explicit > 12000 > 108 Vaporization of colliding solids

Table 1: When implicit/explicit. An impact response of materials.

Velocity Low High

Deformation Global Local

Response time ms - s µs - ms

Strain < 10% > 50%

Strain Rate < 10 s-1 > 10000 s-1

Pressure < Yield Stress 10 - 100 x Yield Stress Table 2: When implicit/explicit. Typical values for Solid Impacts.

3.9 Optimization modules HyperWorks offers both explicit and implicit solvers for optimization. HyperStudy for explicit

and OptiStruct for implicit. HyperMorph is a tool that applies configured shapes to the

original geometry. This thesis will use HyperStudy and HyperMorph.

3.10 Limitations of optimization The maximum number of runs in the DOE will be set to 150 runs. The area for the

optimization was 7mm high and 8 mm wide.


4 FE Model

4.1 Mesh

4.1.1 Previous mesh Previous work have made four types of element sized meshes on the ACP and two types of

mesh on the ACD shown in appendix 10.1, table 16-17.

4.1.2 Thesis mesh This thesis will mimic the mesh from previous model from ANSYS APDL in HyperMesh and

the different types of mesh zones are shown in figure 3.

A mesh evaluation in four steps have been made to find where a refinement of the mesh no

longer makes a significant difference to the results. The original geometry was used for this

evaluation. The ACP and ACD were grouped into different zones dependent on the

significance of the result in the particular zone. The fillet of the ACP was given a zone, named

4. Zone 4 was the zone of interest and will have the finest mesh. Zone 1 was the drill rod on

the ACD and that was the least important of the thesis, this zone will have the same element

size, 1,6*4,9 mm in this evaluation. The shank adapter on the ACD and the zone 2 of the ACP

are the zones where the contact will occur. This zone will have the same size and number of

elements, before the spin, throughout the evaluation. To make the contact possible in

HyperMesh the elements on the shank adapter and the elements of the zone 2 on the ACP

will have the same element size to avoid penetration problems. Zone 3 was the ACP main

volume and will be changed according to previous work values throughout the evaluation.

Original meshes are shown in table 3 and 4.

Name Mesh generation Element size in the body of the piston [mm]

Element size at fillet [mm]

HW_Mesh1 Automesh, spin ~1,8 ~0,5




Table 3: Mesh generation of the ACP.

Figure 3: The different types of mesh zones at the ACP and ACD in this thesis.


Name Mesh generation Element size in the body of the piston[mm]

HW_Mesh1* Automesh, spin* ~1,6*4,9

HW_Mesh2* Automesh, spin* ~1,8

Table 4: Mesh generated on the ACD.

The difference of mesh between these two theses will be discussed in chapter 8. The

element patterns from the ANSYS version 14 model were not possible to copy and export to

HyperMesh because the mesh system do not support the mesh from ANSYS. Table 5 shows a

compilation of the difference in mesh.

This thesis vs. Previous work

Mesh zones Previous works mesh

1 Mesh1*

2 Mesh2*

3 Mesh 1 - 4

4 Mesh 1 - 4 Table 5: A compilation of mesh between analyses.

4.1.2.1 Analysis of mesh Previous work used mesh3 and mesh1* in the report and displayed the results shown in

appendix 10.2, table 18. The focus will be to generate Tresca and von Mises values.


4.1.2.2 Results of mesh analysis To generate geometry in 3D, a spin of 2D elements has been implemented. The number of

elements per revolution will be based on the selected line in figure 4. The diameter of the

ACP tail was 22,48 mm.

Element per revolution =22,48 ∗ π

Element size at fillet(table 3)

The results are shown in table 6.

Mesh 1 Mesh 2 Mesh 3 Mesh 4 Mesh 4b

Elements/revolution 141 353 706 1413 200

Elements/revolution/2 70 176 353 706 Table 6: Element per revolution.

The hardware had significant problems with the total number of elements from these

calculations and therefore the elements per revolution in table 6 were divided by two.

The total numbers of elements in the model are shown in table 7. The hardware had

problem with mesh 4 and an easier spin was made to manage the calculations, mesh 4b.


Elements ACD&ACP 331773 1097830 4046086 28391084 4215200

Elements ACD&ACP/2 167063 547360 2023043 14195542 Table 7: Element in model.

To achieve a converged result a set of meshes was made with the values from table 5. Zone

4 was divided into 5 lines shown in figure 5.

Figure 4: The conductive line from mesh analysis.

Figure 5: The fillet zone 4 on the ACP. Figure 6: Elements in zone 4 with mesh 1.


Table 8 shows the element per line in figure 5 and displayed in figure 6.


1 1 1 1 1 1

2 14 35 70 140 89

3 48 118 235 470 300

4 1 1 2 4 4

5 36 88 176 352 225

Table 8: Element per line.

Parameterizations were made to give the conductive line a specific number of elements. Line

1 and 4 were constrained by surrounding zones. Line 5 was set to have 75% and line 2 to

have 30% of the elements of line 3 shown in figure 7.

In the evaluation for this thesis there have been four different mesh analysis types displayed

in table 9.

Mesh no.

Max Von Mises [MPa]

Location of max stress on fillet, Von Mises [mm]

Difference from previous work [%]

Max Tresca [MPa]

Location of max stress on fillet, Tresca [mm]

Difference from previous work [%]

HW_Mesh1 594,4 8,52 -4,7 646,5 8,52 -4,3

HW_Mesh2 623,8 8,51 0,2 684,4 8,70 1,3

HW_Mesh3 642,3 8,52 3,1 706,0 8,52 4,5

HW_Mesh4 643,7 8,53 3,4 707,5 8,53 4,7 Table 9: Mesh analysis comparing to previous work.

HW_Mesh3 and HW_Mesh4 yield similar results to HW_Mesh2 on von Mises and Tresca.

HW_Mesh3 and HW_Mesh4 take 10+ hours to solve and this makes these meshes

inappropriate for the optimization. The shockwave through the piston were similar whether

HW_Mesh2 or HW_Mesh3 were used. The figure 8-9 is showing the three different principal

stresses in the simulation. HW_Mesh2 will be used to configure the optimization.

Figure 7: Mesh in zone 4.


Figure 9: HW_Mesh3 shockwave, 300µs time-lapse.

Figure 8: HW_Mesh2 shockwave, 300µs time-lapse.


4.1.3 Analysis of spin A spin evaluation in eight steps was made to find where the number of elements per

revolution no longer made a significant difference in the results. The original geometry was

used for this evaluation. Previous work was done in 2D and did not make an evaluation of

this result. In the mesh analysis an exterior line of the ACP was set to be governing for the

whole geometry. This line will be tested in eight different evaluations. The mesh parameters

from the HW_Mesh2 analysis were used for the tests. The conductive line in the geometry is

shown in figure 4.

4.1.3.1 Result of spin analysis The analysis was made with different number of elements per revolution. The number of

elements per revolution was 50, 125, 176 and 250 initially tested. The results gave not an

indication of any convergence so another analysis was made with 325, 400 and 600 elements

per revolution. Finally 285 elements per revolution were tested to see where the

convergence began. Summarizing the analysis gives that 50, 125, 250, 285, 325, 400 and 600

were analyzed. The gap between 125 and 250 was because the original HW_Mesh2 was spun

with 176 elements per revolution is from the mesh analysis shown in table 9. The chosen

numbers in the analysis were to see if a significant difference in the results will occur, values

shown in table 10.

Elements/rev. Maximum stress range Von Mises [MPa]

Location of max stress range on fillet, Von Mises [mm]

Maximum stress range Tresca [MPa]

Location of max stress range on fillet, Tresca [mm]

50 596,5 8,56 653,7 8,56

125 626,4 8,84 684,5 8,84

176 623,8 8,51 684,4 8,70

250 625,3 8,42 687,0 8,42

285 604,7 8,84 662,4 8,84

325 604,9 8,84 662,6 8,84

400 601,9 8,84 659,2 8,84

600 605,7 8,84 663,5 8,84 Table 10: Summary of spin analysis.

In the spin analysis the results of the location of maximum stress range on fillet were the

same at 125, 285, 325, 400 and 600 elements per revolution. The shockwaves through the

piston were similar whether there were 50 or 285 elements per revolution shown in figure

10-11. Differences between the locations of stress range maximum were found in the

evaluation. The value of 285 elements per revolution was to be considered converged. The

figure 10-11 is showing the three different principal stresses in the simulation. With these

two analyses completed, the values this thesis will continue with the combination of

HW_Mesh2 and 285 elements per revolution for the optimization.


Figure 11: 285 elements per revolution, 300µs time-lapse.

Figure 10: 50 elements per revolution, 300µs time-lapse.


4.2 Initial Conditions The shank adapter will be at rest at the initial stage of the simulation, 0 m/s. The ACP will

have a velocity of 9.13 m/s shown in figure 12. The gap will be set to 1µm between the ACP

and the ACD. Fixed support was set to the nodes at the end of the ACD shown in figure 13.

The friction between the ACD and the ACP upon impact was set to µ 1.0 according to

previous work.

Figure 12: Initial Velocity was 9,13 m/s on the ACP.

Figure 13: Nodes where translation in y-axis was locked on the ACD.


4.3 Components The components of the analysis were the impact piston (ACP) and the drill rod and shank

adapter (ACD), figure 14 and more detailed in figure 2.

4.4 Material The material is isotropic, linear elastic material and represents a linear relation between

stress and strain. M1_ELAST is the name for the category of materials in HyperWorks. The

name of material in this thesis will be named A_Steel with the specific values shown in table

11 and software interface in appendix 10.3, figure 32.

Table 11: Key values in the material.

Property Value Unit

Poisson 0,3

Young´s modulus 2,10E+11 Pa

Density 7850 kg/m3

Figure 14: The complete setup with the ACP and ACD.


4.5 Constraints

4.5.1 EngineFile EngineFile is the setup parameter for output file from the solver Radioss. To generate frames

used in for the post-processing Tfreq was set to 2.0 E -006 s.

The setup for Radioss shown in appendix 10.3, figure 33.

Run number: The zero indicates that the engine file reads the HeaderCard for a specific run

number.

T Stop: The duration of simulation.

N Print: The frequency for generating data for post processor.

T File: The start time for the simulation.

The setup for Radioss shown in appendix 10.3, figure 34.

ANIM/DT: The frequency for generating output data for post processor.

ANIM/BRICK/TENS: Generates stress in i-, j-, k - directions for HyperView.

ANIM/KEY2/KEY3: Generate a direct result of von Mises stress in the elements

4.6 Property The impact piston and shank adapter will be set to TYPE14 in HyperWorks. This is the setting

for general solid property sets in HyperWorks. The setting ISOLID, is the elements

formulation how the solid is formed. ISOLID 24 builds the solid with HEPH 8-node solid

element, which is Co-rotational, under-integrated (1 Gauss point) with physical

stabilization. For interface specifics see appendix 10.3, figure 35.

4.7 Contact The previous work defined the contact between the impact piston and the shank adapter in

ANSYS version 14.0 with an Augmented Lagrangian. HyperWorks does not use Augmented

Lagrangian as a contact parameter instead the program uses different types of interfaces.

The contact interface TYPE 7 is used for general purpose interface and this interface can also

simulate all types of impacts between a set of nodes and master surfaces. The stiffness of the

two bodies with interface TYPE 7 is not constant, instead it increases with penetration

preventing the nodes from going through the element surface. This difference of contact

parameters may create a different result and that will be discussed in the chapter 8. For

interface specifics see appendix 10.3, figure 36.


4.7.1 Detach or translate HyperWorks has two different methods of splitting the geometry, detach and translate. The

detach function was used to detach elements from the surrounding structure. The translate

function was used to move entities in a single specified direction. The difference was small

and shown in figure 15-16, the values are MPa.

The original geometry that was imported from ANSYS APDL was made in one geometry. This

thesis will work with the detach function to make the ACP and ACD to individual parts.

Figure 15: ACP geometry with fillet, detach.

Figure 16: ACP geometry with fillet, translate.


4.8 Damping The previous work made an approximation of amplitude decay factor. The value was set to

γ=0.1 in the HHT method in ANSYS, this is a calculation of numerical damping. Altair

Engineering was contacted about the damping issue and two possibilities were made, VIS_F

and VIS_S. VIS_F is critical damping coefficient on interface friction and VIS_S is critical

damping coefficient on interface stiffness. The difference result in VIS_F and VIS_S was less

than 1%. The recommendation from Altair Engineering was to use the VIS_S with the value

0,1 in this thesis.

4.9 Results of model setup The analysis of the previous work resulted in HW_Mesh2, 285 elements per revolution and

VIS_S value 0,1 was to be continued with throughout this thesis for the optimization.


5 Calculation

5.1 Tresca Tresca calculation was not a default output option in HyperWorks. Generating results with

Tresca was a manual operation in the expression builder [6]. From the previous work the

formulation of Tresca was: 𝜎𝑇 = 𝑖(𝜎1 − 𝜎3), 𝑖 = {1 𝑖𝑓 𝜎1 + 𝜎3 ≥ 0

−1 𝑖𝑓 𝜎1 + 𝜎3 < 0

The Tresca equation is expressed in appendix 10.3, figure 37.

In expression builder in appendix 10.3, figure 35, T1.C8 is the expression for principal stress

in the 1st direction and T1.C10 is the 3rd direction. The “abs” is the expression is for absolute

value.


6 Optimization

6.1 Model The setup used for the optimization were HW_Mesh2 and 285 elements per revolution. The

geometry was altered to 90 degrees to make the optimization faster. The fillet was altered to

a chamfer to simplify the topology. Shapes will be added to the geometry and the

optimization will work to alter the starting geometry towards the shapes. The starting

geometry of the chamfer is displayed in figure 17.

6.2 2D-Shell The 2D shell was added on the face of the elements at the chamfer, marked green in picture

18. To reduce the amount of calculations in the optimization, the elements monitored were

all within the 2D shell.

Figure 17: Starting geometry for the optimization.

Figure 18: 2D – shell to monitor the stress range.


6.3 Morphing Morphing will be performed by stretching the elements at the chamfer shown in figure 19.

The elements were stretched towards the line and the tool HyperMorph work towards

altering all elements as equally as possible.

6.4 Fourier curves For configuring the optimization a set of different shapes will be made. The theory of the

shapes were based on the Fourier principal [7]. The principal shows that all type of lines can

be expressed with a set of sine-, and cos-curves which are different in amplitude and phase.

Figure 19: Morphing procedure to stretch the elements as equally as possible.


6.5 Shapes Three different types of shapes were applied to the model according to Fourier principal.

Shapes are shown in figure 20 – 22.

Figure 21: Shape 2, 2 mm amplitude sine function.

Figure 20: Shape 1, 2mm amplitude sine function.


The number of runs increases exponentially with each added shape. The limitation of the

thesis was to have a maximum of 150 runs. Therefore three shapes in five levels will generate

125 runs. Due to limitations in software, shape 3, figure 22, was not able to be given the

amplitude of 2 mm. To avoid a sharp edge, a spline was created and spun to create a surface

of the chamfer. Sharp edge is shown in figure 23.

Figure 22: Shape 3, 1 mm amplitude sine function.

Sharp edge

Figure 23: Sharp edge was now made as a spline to avoid high stress range.


6.6 Approach of optimization HyperStudy has three types of approaches to make an optimization. The approaches were

DOE, Optimization and Stochastic shown in figure 24. For all approaches a script was written

in HyperMath. This script will work as the response for all approaches. For the study setup a

nominal run was chosen for the thesis. This system runs the initial values from zero to one.

See appendix 10.3, figure 38.

Figure 14: Approaches for optimization in HyperStudy. Three different steps.


Figure 25: Approach: DOE Fit Optimization.

6.6.1 DOE - Fit - Optimization The DOE - Fit - Optimization approaches will be used for the optimization in this thesis. Three

shapes with five levels each will result in 125 different runs with DOE shown in table 12. The

DOE will extract the element with the

highest stress range from every run.

Shape 1 Shape 2 Shape 3

0,00 0,00 0,00

0,25 0,25 0,25

0,50 0,50 0,50

0,75 0,75 0,75

1,00 1,00 1,00 Table 12: Step for DOE in this thesis.

The DOE type was Full Factorial and the operation is shown in figure 25. Full factorial was

used since it allows more than three levels of each shape.

The Fit approach was a study made to identify the global trend of the results from the DOE.

When irregular and uneven results, optimization algorithms have trouble locating global

optimum and work towards local max/min. This makes the algorithm inefficient and the Fit

was useful to help the optimization work towards finding global max/min. The Fit approach is

shown in figure 26.

Figure 27: Fit approach. Figure 26: Approach: DOE Fit Optimization.


The Optimization process is shown in figure 27. The method used for the optimization step

was a genetic algorithm and the optimization tool works to find the desired global optimum.

6.6.1.1 Response Script The script myFunc will retrieve the maximum compression and tensile stress from the

elements 2 – 1289 in every time step, as shown in appendix 10.3, row 5, 8-9

Figure 27: Approach DOE Fit Optimization.


6.6.1.2 Full Factorial Full factorial design of experience (DOE) systematically combines every possible combination

of design variables and levels. An example is shown in table 13–14.

6.6.2 Fit Fit have four different types of methods, see appendix 10.3. MLSM was chosen since it was

most compatible with a prior DOE approach. Default configuration of the MLSM was used.

6.6.2.1 Moving least squares This method is a generalization of the weighted least squares method [8]. MLSM is an

approximation building technique. The main difference done in the generalization is that the

weight of approximated points differs depending on the distance to the closest sampling

point from the DOE.

Run number A B C

1 1 1 1

2 1 1 2

3 1 1 3

4 1 2 1

5 1 2 2

6 1 2 3

7 2 1 1

8 2 1 2

9 2 1 3

10 2 2 1

11 2 2 2

12 2 2 3

Total number of design variables 8

Number of design variables with two levels 2

Number of design variables with three levels 1

Total number of runs 22*31=12

Table 14: Equation for number of runs in DOE.

Table 13: DOE combination example.


6.6.3 Optimization HyperStudy have 10 different types of optimization algorithms. Together with the Applied

Mechanics department the genetic algorithm was chosen since earlier experiences in other

genetic algorithms. Default configuration of the GA was used.

6.6.3.1 Genetic algorithm The GA is an automated learning technique model based on the Darwin’s evolutionary

theory and the natural selection [9]. The workflow of the GA can be seen in figure 28.

The optimization approach will not genera a population when running the GA after finishing

a DOE or stochastic approach, the algorithm will use prior results from approaches as

population. Generating a population will only occur when running an optimization approach

directly after the study setup.

In general the GA works similar to natural selection, where the individuals are different

combination of design parameters and constraints. These individuals with different attributes

represent the population. One individual is then matched and compared with another

individual. The fittest competitor of the two will be evaluated if it fits the termination

criteria. If it does, the optimization ends with the victor as the optimum. If the criteria are

not met, then the victor will be selected as a parent for the next generation of individuals.

The offspring will then be matched against another individual and evaluated. This is repeated

until an individual meets the termination criteria. [10]. The GA in HyperStudy was by itself,

Start

Generate Population

Submit Analysis

Calculate Fitness

Elitist Policy

Apply Operators

Select Parents

Define Operators

Crossover Mutation

Objectives and Constraints

Stop

Termination Criteria

No

Yes

Figure 28: The calculation path for the Genetic algorithm in HyperStudy.


computationally inefficient and was therefore supported with a local search algorithm, called

Hooke-Jeeves Method [11].

7 Result of Optimization The optimization resulted in a shape that lowered the stress 37,1 % from the original

chamfer shaped geometry. However, the stress was not lowered below 622 MPa which was

the stress range from the original fillet. The configuration of shapes is presented in table 15,

and the geometry in figure 29.

S.1 S.2 S.3 MPa Fit approach, MPa

0,00 0,00 0,00 1146,15 1145,80

0,25 0,75 0,00 717,42 720,73

0,24 0,91 0,00 687,22 687,22 Table 15: Results from optimization in HyperStudy.

Figure 29: The ACPs optimized geometry.


This 3D-plot in figure 30, shows plots of the optimization. The axis represents the three

shapes and the percentage they are applied. The optimization GA takes smaller steps with

each run and increased the number of runs around the global optimum at 0,25 on axis 1.S,

0,90 on 2.S and 0,00 on 3.S.

The graph in figure 31 shows that the optimization has found optimum and converged within

our levels of design parameters. The small variation of stress range in the consecutive

iterations was to be considered a converged solution.

Figure 20: 3D-Plot of Optimization.

Figure 31: Graph of Max Stress Range of each iteration of Optimization approach.


8 Discussion HyperWorks and ANSYS APDL were incompatible to export/import complete FE models

between. This thesis can´t copy the previous mesh pattern and that might have an impact on

the results. Therefore the meshes will not be identical and will generate different values.

Zone 1 have the same element size throughout the thesis, and have same element size as

previous work. Zone 2 includes the shank adapter and the edge of the ACP. These areas were

in the same zone to help HyperMesh to avoid penetration. Zone 3 was generally speaking the

same mesh but, this thesis will use mesh 1 throughout the analysis to hold the number of

elements down in the model. Zone 4 was our idea on how the mesh from previous work

could be transferred in the best way to HyperWorks from ANSYS APDL.

A decision to try 285, 325, 400 and 600 elements per revolution was because uneven values

occurred in the stress range analysis.

A problem that occurred when using the translate option was that if the gap was set to 1 µm

the solver will generate errors due to having penetrating nodes at the start of the run. This

hasn’t been able to be fixed with finer tolerances and element sizes.

The thesis did not make any improvement of the values from the previous work. HyperWorks

show that it has potential to make optimizations to different types of geometries and

problems. For future setup of problems of this type of characteristics, more shapes and more

sublevels can be added to help the optimization algorithm find the global optimum.

The overall impression of the software is that it is very extensive. Implicit or explicit runs can

be made, scripts can be made for extracting any value from the model, different types of

optimization can be made with a number of different algorithms and it could also generate

calculations for processing results.

The steps that were taken for the optimization in HyperStudy was made together with

Robert Pettersson, Specialist – Mechanical Analysis on Applied Mechanics and Erik

Magnemark, Application Engineer on Altair Engineering.


9 Reference 1. Mining weekly: Study identifies Sandvik, Atlas Copco as leading suppliers of

underground mobile equipment, Posted 2012-10-12.

http://www.miningweekly.com/article/three-companies-dominate-underground-

mining-mobile-equipment-market-2012-10-12

2. Kenneth Weddfelt, 2001, BBX 262 radieutformning vid kolvsvans, Internal documents

at Atlas Copco.

3. Kenneth Weddfelt, 2004, BBX 270 radieutformning vid kolvsvans, Internal documents

at Atlas Copco.

4. J.S Sun, K.H Lee, H.P Lee, 2000, Journal of materials processing technology, Elsevier

B.V.

5. ANSYS costumer training material, Introduction to Explicit Dynamics, Release 13.0

December 2010.

6. William F. Hosford, 2010, Mechanical behaviors of materials second edition,

Cambridge University press.

7. Donald A McQuarrie, 2003, Mathematical methods for scientists and engineers,

University science books.

8. Robert D. Cook, David S. Malkus, Michael E. Plesha, Robert J. Witt, 2002, Concepts

and applications of finite element analysis fourth edition, John Wiley & Sons, INC.

9. Charles Darwin, 2005, On the origin of species, Natur och Kultur.

10. Melanie Mitchell, 1999, An introduction to genetic algorithm, Massachusetts Institute

of Technology.

11. L. L. Lai and T. F. Chan, 2007, Distributed Generation: Induction and Permanent

Magnet Generator, John Wiley & Sons, INC.

http://www.miningweekly.com/article/three-companies-dominate-underground-mining-mobile-equipment-market-2012-10-12

http://www.miningweekly.com/article/three-companies-dominate-underground-mining-mobile-equipment-market-2012-10-12


10 Appendix

10.1 Previous Mesh Name Mesh generation Element size in the body

of the piston [mm] Element size at fillet [mm]

Mesh1 smrt,1; Irefine, x,,,1,1, clean

~1,8 ~0,5

Mesh2 smrt,1; Irefine, x,,,1,3 ,clean; Irefine, x,,, 1,1,clean

~1,8 ~0,2

Mesh3 smrt,1; arefine, all,,,1,1, clean; Irefine, x,,,1,3,clean; Irefine, x,,,1,1,clean

~0,9 ~0,1

Mesh4 smrt,1; arefine, all,,,1,1, clean; Irefine, x,,,1,3,clean; Irefine, x,,,1,1,clean

~0,5 ~0,05

Table 16: Meshes used to model the piston. Irefine is a mesh refinement at lines and arefine is a mesh refinement at areas. X is the line number in the ANSYS model associated with the fillet.

Name Mesh generation Element size in the body of the piston[mm]

Mesh1* Mapped meshing ~1,6*4,9

Mesh2* smrt,1 ~1,8

Table 17: Meshes used to model shank adapter and drill rod.

10.2 Previous results

Previous work

Stress measure Maximum stress range at a point on the fillet [MPa]

Location, s, of the maximum stress range [mm]

Signed Tresca 675,3 8,57

Signed von Mises 622,3 8,63 Table 18: Results from mesh3 and mesh1*.


10.3 Software specifics

Figure 33: The interface in HyperMesh for Engine file, general setup.

Figure 32: The interface in HyperMesh for material properties.


Figure 34: The interface in HyperMesh for EngineFile, animation setup.


Figure 35: The interface in HyperMesh for geometry property.

Figure 36: The interface in HyperView for Tresca formulation.


Figure 37: The interface in HyperMesh for contact.


On row 10 the command is given to calculate the stress range. The elements selected in the

script were the 2D shell. This will make the optimization run more efficient.

Figure 38: The interface in HyperMath for the 2D-shell script.

Figure 39: The interface in HyperStudy for Study evaluation setup.

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