symme y
S
S
A icle
Design P ocedu e o a Topologically Op imized
Scoo e F ame Pa
Lukas Janca 1, Ma ek Pagac 2, Jakub Mesicek 2and Pe S e ek 2,*
1Depa men o Machine Pa s and Mechanisms, Facul y o Mechanical Enginee ing,
VSB-Technical Uni e si y o Os a a, 708 33 Os a a, Czech Republic; [email p o ec ed]
2Depa men o Machining, Assembly and Enginee ing Me ology, Facul y o Mechanical Enginee ing,
VSB-Technical Uni e si y o Os a a, 708 33 Os a a, Czech Republic; [email p o ec ed] (M.P.);
[email p o ec ed] (J.M.)
*Co espondence: pe [email p o ec ed]
Recei ed: 31 Janua y 2020; Accep ed: 8 Ap il 2020; Published: 6 May 2020
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Abs ac :
This a icle desc ibes he design p ocedu e o a opologically op imized scoo e ame pa .
I is he ea heel o he ame, one o he ou main pa s o a scoo e made wi h s ainless s eel 3D
p in ing. The i s pa o he a icle deals wi h he design a ea de ini ion and he de e mina ion o load
cases o opology calcula ion. The second pa desc ibes he p ocess o he opology op imiza ion
i sel and he c ea ion o he olume body based on he calcula ion esul s. Finally, he inal con ol
using an FEM (Fini e Elemen Me hod) analysis and op imiza ion o c ea ed Compu e -Aided Design
(CAD) da a is shown. Pa o he a icle is also a e iew o pa ial i e a ions and esul ing e sions o
he designed pa . Symme y was used o de ine bounda y condi ions, which led o compu ing ime
sa ings, as well as du ing he CAD model c ea ion, whe e non-pa ame ic su aces we e mi o ed o
sho en he design ime.
Keywo ds: opology op imiza ion; 3D p in ing; scoo e ; SLM; NURBs; FEM
1. In oduc ion
The de elopmen o addi i e echnologies (3D p in ing) has g own conside ably in he a ea o
c ea i e design and he mode n echnical app oach o componen design. Th ee-dimensional p in ing
has changed he mindse o designe s and enginee s who can apply new echnological design p inciples
wi h ega d o he echnological p oduc ion p ocess and ake ad an age o he possibili y o ligh ening
pa s designed especially o he au omo i e and ae ospace indus ies.
A mode n design app oach allows designe s o design componen s ha ha e a so-called bionic
shape [
1
]. This is c ea ed by ee- o m modelling in specialized CAD so wa e. Compa ed o
con en ional echnologies, i makes i possible o design pa s ha e y o en ha e su aces which a e
ma hema ically di icul o de ine. In p ac ice, such pa s canno be p oduced wi hou simul aneous
i e-axis milling and in many cases, such as he p oduc ion o hollow me al ames [
2
], 3D p in ing
is necessa y as hey canno be p oduced by ano he echnology. Ano he ypical example is la ice
s uc u es. They a e designed o abso b impac ene gy [
3
,
4
], educe ib a ion and noise, o se e as a
he mal conduc o . These pa s canno be manu ac u ed in any o he way han by 3D p in ing.
When we alk abou bionic design, we mean shapes inspi ed by na u e. The cons uc ions may
ha e a non- echnical shape esembling biological s uc u es, such as ee b anch s uc u es, he oo
sys em, skele al shapes, o animal bodies [
5
,
6
]. Ma e ial is in ol ed only whe e i is s ic ly necessa y
due o bounda y condi ions. E e y designed model wi h bionic cons uc ion is ho oughly checked
by an FEM analysis and specialized so wa e is used o he calcula ion. The designe de ines he
ma e ial based on he design a ea and only whe e i ul ills i s exclusi e pu pose in e ms o mechanical
Symme y 2020,12, 755; doi:10.3390/sym12050755 www.mdpi.com/jou nal/symme y
Symme y 2020,12, 755 2 o 14
p ope ies. This p ocess is called opological op imiza ion, whose de ailed p ocedu e is p esen ed la e
in his pape and is ep esen ed on a scoo e oo model.
Wi hin he addi i e manu ac u ing labo a o y P o oLab, which deals wi h 3D p in ing and CAD
design, he opologically op imized scoo e was designed and 3D p in ed. The aim was o design and
de elop a scoo e ame ha is opologically op imized wi h a bionic shape and made by addi i e
manu ac u ing. Fu he mo e, he goal was o achie e weigh educ ion o e con en ional scoo e s.
In Figu e 1, he whole design p ocess wo k low is shown.
Symme y 2020, 12, x FOR PEER REVIEW 2 o 14
due o bounda y condi ions. E e y designed model wi h bionic cons uc ion is ho oughly checked
by an FEM analysis and specialized so wa e is used o he calcula ion. The designe de ines he
ma e ial based on he design a ea and only whe e i ul ills i s exclusi e pu pose in e ms o
mechanical p ope ies. This p ocess is called opological op imiza ion, whose de ailed p ocedu e is
p esen ed la e in his pape and is ep esen ed on a scoo e oo model.
Wi hin he addi i e manu ac u ing labo a o y P o oLab, which deals wi h 3D p in ing and CAD
design, he opologically op imized scoo e was designed and 3D p in ed. The aim was o design and
de elop a scoo e ame ha is opologically op imized wi h a bionic shape and made by addi i e
manu ac u ing. Fu he mo e, he goal was o achie e weigh educ ion o e con en ional scoo e s.
In Figu e 1, he whole design p ocess wo k low is shown.
Du ing he pa ’s design, wo imes symme y was used. Fi s , when bounda y condi ions we e
de ined, he symme y cons ain was used. This bounda y condi ion is used o c ea e op imized
shapes wi h nea ly symme ic esul s. I also sa es compu ing ime, as only hal o he op imiza ion
ask is sol ed. Secondly, symme y was used du ing CAD model c ea ion, whe e non-pa ame ic
su aces we e mi o ed o sa e he design ime and o ensu e he symme y o he pa .
The esul is a unc ional p o o ype o he scoo e shown in Figu e 2, which has a bionic ame
p in ed wi h s ainless s eel. A 25% weigh sa ing was achie ed compa ed o con en ional scoo e
ames while main aining su icien igidi y. The ame consis s o 4 s ainless s eel elemen s and 4
ca bon composi e p o iles joined oge he by gluing. P in ed me al elemen s we e pos -p ocessed by
umbling in ce amic elemen s o ge a smoo h appea ance. The la ge on ame pa was di ided
in o 4 sub-pa s be o e p in ing, wi h ega ds o he size o he building chambe . These pa s we e
welded oge he a e wa ds using he TIG ( ungs en ine gas) welding me hod.
Figu e 1. Block diag am o he op imiza ion wo k low.
Figu e 1. Block diag am o he op imiza ion wo k low.
Du ing he pa ’s design, wo imes symme y was used. Fi s , when bounda y condi ions we e
de ined, he symme y cons ain was used. This bounda y condi ion is used o c ea e op imized
shapes wi h nea ly symme ic esul s. I also sa es compu ing ime, as only hal o he op imiza ion
ask is sol ed. Secondly, symme y was used du ing CAD model c ea ion, whe e non-pa ame ic
su aces we e mi o ed o sa e he design ime and o ensu e he symme y o he pa .
The esul is a unc ional p o o ype o he scoo e shown in Figu e 2, which has a bionic ame
p in ed wi h s ainless s eel. A 25% weigh sa ing was achie ed compa ed o con en ional scoo e
ames while main aining su icien igidi y. The ame consis s o 4 s ainless s eel elemen s and
4 ca bon composi e p o iles joined oge he by gluing. P in ed me al elemen s we e pos -p ocessed by
umbling in ce amic elemen s o ge a smoo h appea ance. The la ge on ame pa was di ided in o
4 sub-pa s be o e p in ing, wi h ega ds o he size o he building chambe . These pa s we e welded
oge he a e wa ds using he TIG ( ungs en ine gas) welding me hod.
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Symme y 2020, 12, x FOR PEER REVIEW 3 o 14
The aim o his a icle was o show he op imiza ion p ocess on one o he ame pa s. The ea
heel o he ame was selec ed, which joins he p o iles unde he s ep and ea wheel o k p o ile.
The pape deals wi h he design o load pa ame e s, analysis se ings and CAD model c ea ion. Nex ,
he subsequen manu ac u ing me hod o he pa is desc ibed.
Figu e 2. Th ee-dimensional p in ed scoo e wi h bionic ame.
2. Ma e ials and Me hods
2.1. Design Va ian s
The design o he heel shape and appea ance was based on he i s design ske ches o he whole
scoo e , so ha i s design ma ched he es o he cons uc ion while mee ing he necessa y s eng h
pa ame e s. Two de elopmen al a ian s o he heel we e de eloped. The i s is a hollow shell wi h
an in e nal space illed wi h la ice s uc u e. In e nal la ice in ill s eng hens he s uc u e wi h a
minimal weigh inc ease. As such, a e ahed al la ice pa e n was chosen [7]. The e we e also
aes he ic iewpo s designed, h ough which he la ice s uc u e inside can be seen (see Figu e 3).
Figu e 3. Fi s heel e sion wi h la ice s uc u e inside.
A second a ian , an o ganic and pa ially shell-shaped model, was conside ed [8]. Finally, a
bionic shape was chosen o p oduc ion due o he op ically slimme design unde lining he ligh ness
o he scoo e ame. Bionic shape means an o ganic, biologically inspi ed design, which esembles
sys ems ound in na u e (see Figu e 4).
Figu e 2. Th ee-dimensional p in ed scoo e wi h bionic ame.
The aim o his a icle was o show he op imiza ion p ocess on one o he ame pa s. The ea
heel o he ame was selec ed, which joins he p o iles unde he s ep and ea wheel o k p o ile.
The pape deals wi h he design o load pa ame e s, analysis se ings and CAD model c ea ion. Nex ,
he subsequen manu ac u ing me hod o he pa is desc ibed.
2. Ma e ials and Me hods
2.1. Design Va ian s
The design o he heel shape and appea ance was based on he i s design ske ches o he whole
scoo e , so ha i s design ma ched he es o he cons uc ion while mee ing he necessa y s eng h
pa ame e s. Two de elopmen al a ian s o he heel we e de eloped. The i s is a hollow shell wi h
an in e nal space illed wi h la ice s uc u e. In e nal la ice in ill s eng hens he s uc u e wi h
a minimal weigh inc ease. As such, a e ahed al la ice pa e n was chosen [
7
]. The e we e also
aes he ic iewpo s designed, h ough which he la ice s uc u e inside can be seen (see Figu e 3).
Symme y 2020, 12, x FOR PEER REVIEW 3 o 14
The aim o his a icle was o show he op imiza ion p ocess on one o he ame pa s. The ea
heel o he ame was selec ed, which joins he p o iles unde he s ep and ea wheel o k p o ile.
The pape deals wi h he design o load pa ame e s, analysis se ings and CAD model c ea ion. Nex ,
he subsequen manu ac u ing me hod o he pa is desc ibed.
Figu e 2. Th ee-dimensional p in ed scoo e wi h bionic ame.
2. Ma e ials and Me hods
2.1. Design Va ian s
The design o he heel shape and appea ance was based on he i s design ske ches o he whole
scoo e , so ha i s design ma ched he es o he cons uc ion while mee ing he necessa y s eng h
pa ame e s. Two de elopmen al a ian s o he heel we e de eloped. The i s is a hollow shell wi h
an in e nal space illed wi h la ice s uc u e. In e nal la ice in ill s eng hens he s uc u e wi h a
minimal weigh inc ease. As such, a e ahed al la ice pa e n was chosen [7]. The e we e also
aes he ic iewpo s designed, h ough which he la ice s uc u e inside can be seen (see Figu e 3).
Figu e 3. Fi s heel e sion wi h la ice s uc u e inside.
A second a ian , an o ganic and pa ially shell-shaped model, was conside ed [8]. Finally, a
bionic shape was chosen o p oduc ion due o he op ically slimme design unde lining he ligh ness
o he scoo e ame. Bionic shape means an o ganic, biologically inspi ed design, which esembles
sys ems ound in na u e (see Figu e 4).
Figu e 3. Fi s heel e sion wi h la ice s uc u e inside.
A second a ian , an o ganic and pa ially shell-shaped model, was conside ed [
8
]. Finally,
a bionic shape was chosen o p oduc ion due o he op ically slimme design unde lining he ligh ness
o he scoo e ame. Bionic shape means an o ganic, biologically inspi ed design, which esembles
sys ems ound in na u e (see Figu e 4).
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Figu e 4. Second heel e sion wi h bionic design.
2.2. Design A ea
The i s bounda y condi ion o he opological op imiza ion is o de e mine he design a ea. I
is a geome ically de e mined space in which op imiza ion can ake place, wi h espec o he
maximum olume in which he u u e analysis solu ion mus be loca ed. The limi ing ac o s in he
design a ea c ea ion a e, in pa icula , he maximum possible ins alla ion dimensions, in which he
pa will s ill be able o be moun ed wi h no collisions wi h he su oundings. In essence, he esul ing
design a ea i sel should be a moun able and usable pa ha will pe o m i s unc ion and will no
in e e e wi h he es o he mechanism [9].
The goal is o make his a ea as oluminous as possible o analysis, allowing so wa e o be as
spacious as possible. Fi s , he design a ea o he en i e scoo e ame, shown in Figu e 5, was
de eloped. This espec s he necessa y geome ic pa ame e s such as o k il , oo ba heigh , chassis
g ound clea ance, and wheelbase.
Figu e 5. F ame design a ea wi h heel loca ion shown.
This design a ea was hen di ided in o pa s co esponding o indi idual ame pa s. In he
case o he ea heel, he limi ing geome ical condi ion was he o e all wid h. As such, a 100 mm
maximum was de e mined. When exceeded, i would be no longe com o able o kick wi h he oo
while iding. In addi ion, he ea wheel cu -ou moun ing holes o la e bonding o he connec ing
p o iles and he p o ec i e ba o p o ec he oo om en e ing he wheel when he oo slips we e
designed.
A e de ining hese equi emen s, he design a ea o he heel was inally adjus ed o he shape
seen in Figu e 6.
Figu e 4. Second heel e sion wi h bionic design.
2.2. Design A ea
The i s bounda y condi ion o he opological op imiza ion is o de e mine he design a ea. I is
a geome ically de e mined space in which op imiza ion can ake place, wi h espec o he maximum
olume in which he u u e analysis solu ion mus be loca ed. The limi ing ac o s in he design a ea
c ea ion a e, in pa icula , he maximum possible ins alla ion dimensions, in which he pa will s ill be
able o be moun ed wi h no collisions wi h he su oundings. In essence, he esul ing design a ea
i sel should be a moun able and usable pa ha will pe o m i s unc ion and will no in e e e wi h
he es o he mechanism [9].
The goal is o make his a ea as oluminous as possible o analysis, allowing so wa e o be as
spacious as possible. Fi s , he design a ea o he en i e scoo e ame, shown in Figu e 5, was de eloped.
This espec s he necessa y geome ic pa ame e s such as o k il , oo ba heigh , chassis g ound
clea ance, and wheelbase.
Symme y 2020, 12, x FOR PEER REVIEW 4 o 14
Figu e 4. Second heel e sion wi h bionic design.
2.2. Design A ea
The i s bounda y condi ion o he opological op imiza ion is o de e mine he design a ea. I
is a geome ically de e mined space in which op imiza ion can ake place, wi h espec o he
maximum olume in which he u u e analysis solu ion mus be loca ed. The limi ing ac o s in he
design a ea c ea ion a e, in pa icula , he maximum possible ins alla ion dimensions, in which he
pa will s ill be able o be moun ed wi h no collisions wi h he su oundings. In essence, he esul ing
design a ea i sel should be a moun able and usable pa ha will pe o m i s unc ion and will no
in e e e wi h he es o he mechanism [9].
The goal is o make his a ea as oluminous as possible o analysis, allowing so wa e o be as
spacious as possible. Fi s , he design a ea o he en i e scoo e ame, shown in Figu e 5, was
de eloped. This espec s he necessa y geome ic pa ame e s such as o k il , oo ba heigh , chassis
g ound clea ance, and wheelbase.
Figu e 5. F ame design a ea wi h heel loca ion shown.
This design a ea was hen di ided in o pa s co esponding o indi idual ame pa s. In he
case o he ea heel, he limi ing geome ical condi ion was he o e all wid h. As such, a 100 mm
maximum was de e mined. When exceeded, i would be no longe com o able o kick wi h he oo
while iding. In addi ion, he ea wheel cu -ou moun ing holes o la e bonding o he connec ing
p o iles and he p o ec i e ba o p o ec he oo om en e ing he wheel when he oo slips we e
designed.
A e de ining hese equi emen s, he design a ea o he heel was inally adjus ed o he shape
seen in Figu e 6.
Figu e 5. F ame design a ea wi h heel loca ion shown.
This design a ea was hen di ided in o pa s co esponding o indi idual ame pa s. In he case
o he ea heel, he limi ing geome ical condi ion was he o e all wid h. As such, a 100 mm maximum
was de e mined. When exceeded, i would be no longe com o able o kick wi h he oo while iding.
In addi ion, he ea wheel cu -ou moun ing holes o la e bonding o he connec ing p o iles and he
p o ec i e ba o p o ec he oo om en e ing he wheel when he oo slips we e designed.
A e de ining hese equi emen s, he design a ea o he heel was inally adjus ed o he shape
seen in Figu e 6.
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Figu e 6. Modi ied heel design a ea.
2.3. Load Cases
Fo opological analysis, i is necessa y o de ine he load cases, o which he calcula ion and
hen he FEM analysis will be calcula ed [10]. These load cases we e c ea ed o he en i e scoo e
ame and hen e e enced o he heel pa i sel . Fou c i ical s a es we e de ined in o al.
2.3.1. Ve ical Impac
This load case is conside ed as a e ical impac caused by ee all o he scoo e wi h a ide
om a heigh o 1 m. I simula es a jump wi h a scoo e , and subsequen ly, a s eep c ossing o an
obs acle like a ke b o hump. A 75 kg ide imposes a s a ic load o 736 N on he ame, a alue which
has been mul iplied by a dynamic load ac o o 3 g, esul ing in a loadcase alue o 2210 N.
2.3.2. B aking
The load case was simula ed as b aking wi h a slowdown o 5 m·s−2, when he mass is ans e ed
o he on wheel and mainly he on ame pa and he o k neck is s essed.
2.3.3. D i ing on a Fla wi h Allowed De lec ion
This case should ake in o accoun he maximum possible de lec ion o he ame unde he load
o he ide in o de o a oid excessi e ame dis o ion while iding and collision o he chassis wi h
he oad du ing kicking. The case was de e mined expe imen ally by measu ing he p ope ies o a
con en ional scoo e , whe e he maximum de lec ion o he lowe chassis unde he load o a ide
weighing 80 kg was se a 11 mm while main aining a minimum chassis clea ance o 60 mm.
2.3.4. To sion
This case akes in o accoun he o sional s i ness o he scoo e so ha he ame is no wis ed
and de o med when co ne ing. I was also de e mined expe imen ally on a con en ional ame. The
ame was i mly ixed and he on o k was g adually loaded o he maximum 100 N o ce
pe pendicula o he ans e se symme y plane o he ame. The ame de lec ion was hen
measu ed a he neck. A 100 N, a maximum allowable neck de lec ion o 30 mm was de e mined.
The expe imen is shown in Figu e 7.
Figu e 6. Modi ied heel design a ea.
2.3. Load Cases
Fo opological analysis, i is necessa y o de ine he load cases, o which he calcula ion and hen
he FEM analysis will be calcula ed [
10
]. These load cases we e c ea ed o he en i e scoo e ame and
hen e e enced o he heel pa i sel . Fou c i ical s a es we e de ined in o al.
2.3.1. Ve ical Impac
This load case is conside ed as a e ical impac caused by ee all o he scoo e wi h a ide om
a heigh o 1 m. I simula es a jump wi h a scoo e , and subsequen ly, a s eep c ossing o an obs acle
like a ke b o hump. A 75 kg ide imposes a s a ic load o 736 N on he ame, a alue which has been
mul iplied by a dynamic load ac o o 3 g, esul ing in a loadcase alue o 2210 N.
2.3.2. B aking
The load case was simula ed as b aking wi h a slowdown o 5 m
·
s
−2
, when he mass is ans e ed
o he on wheel and mainly he on ame pa and he o k neck is s essed.
2.3.3. D i ing on a Fla wi h Allowed De lec ion
This case should ake in o accoun he maximum possible de lec ion o he ame unde he load
o he ide in o de o a oid excessi e ame dis o ion while iding and collision o he chassis wi h
he oad du ing kicking. The case was de e mined expe imen ally by measu ing he p ope ies o a
con en ional scoo e , whe e he maximum de lec ion o he lowe chassis unde he load o a ide
weighing 80 kg was se a 11 mm while main aining a minimum chassis clea ance o 60 mm.
2.3.4. To sion
This case akes in o accoun he o sional s i ness o he scoo e so ha he ame is no wis ed and
de o med when co ne ing. I was also de e mined expe imen ally on a con en ional ame. The ame
was i mly ixed and he on o k was g adually loaded o he maximum 100 N o ce pe pendicula
o he ans e se symme y plane o he ame. The ame de lec ion was hen measu ed a he neck.
A 100 N, a maximum allowable neck de lec ion o 30 mm was de e mined. The expe imen is shown
in Figu e 7.

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Figu e 7. To sion measu emen expe imen .
2.3.5. Final Load Case
The esul ing ep esen a i e load case was de e mined a e se e al analyses o e lec he c i ical
s ess o he heel pa . I consis s o a combina ion o e ical impac and o sion, wi h maximum
de lec ion checked a e analyses. Basically, b aking was elimina ed because i mainly s ains he
on o he ame and elie es he ea .
The suppo pa e n in he compu ing model is shown in Figu e 8. The heel is clamped om one
ea slee e, which is ixed. The second ea slee e has he abili y o mo e and o a e in i s axis
(sliding), bu no pe pendicula o he axis (i ep esen s he suppo in he ea wheel). One on
slee e is le loose and he o he is loaded wi h a o ce on he leng h equal o he dis ance o he s ep
cen e. This o ce simula es he load o e ical impac , explained in Sec ion 2.3.1, wi h he ide
s anding une enly on he scoo e axis, ep esen ing he o sion. The s a ic o ce in one a m is
inc eased wi h a dynamic load ac o o 3 g o 2210 N.
Figu e 8. Heel load case wi h o ce and suppo s.
2.3.6. Ma e ial
Fo he co ec analysis se ing, i is also necessa y o know he ma e ial om which he
op imized componen will be manu ac u ed. The heel is made o 316 L s ainless s eel. The pa will
be p in ed om a omised powde supplied by he machine manu ac u e , RENISHAW. An
ad an age o he powde -p in ed pa is he imp o ed mechanical p ope ies in compa ison wi h he
same ma e ial in he o m o me allu gical p e o m p oduc s, especially Yield S eng h and Tensile
S eng h [11]. Table 1 lis s he impo an mechanical p ope ies o 316 L-p in ed ma e ial [12].
Table 1. Mechanical p ope ies o 316 L addi i ely manu ac u ed componen s.
S eel 316 L—3D P in ed Uppe Tensile S eng h (UTS)
As Buil
Ho izon al di ec ion (XY)
676 MPa ± 2 MPa
Figu e 7. To sion measu emen expe imen .
2.3.5. Final Load Case
The esul ing ep esen a i e load case was de e mined a e se e al analyses o e lec he c i ical
s ess o he heel pa . I consis s o a combina ion o e ical impac and o sion, wi h maximum
de lec ion checked a e analyses. Basically, b aking was elimina ed because i mainly s ains he on
o he ame and elie es he ea .
The suppo pa e n in he compu ing model is shown in Figu e 8. The heel is clamped om one
ea slee e, which is ixed. The second ea slee e has he abili y o mo e and o a e in i s axis (sliding),
bu no pe pendicula o he axis (i ep esen s he suppo in he ea wheel). One on slee e is
le loose and he o he is loaded wi h a o ce on he leng h equal o he dis ance o he s ep cen e.
This o ce simula es he load o e ical impac , explained in Sec ion 2.3.1, wi h he ide s anding
une enly on he scoo e axis, ep esen ing he o sion. The s a ic o ce in one a m is inc eased wi h a
dynamic load ac o o 3 g o 2210 N.
Symme y 2020, 12, x FOR PEER REVIEW 6 o 14
Figu e 7. To sion measu emen expe imen .
2.3.5. Final Load Case
The esul ing ep esen a i e load case was de e mined a e se e al analyses o e lec he c i ical
s ess o he heel pa . I consis s o a combina ion o e ical impac and o sion, wi h maximum
de lec ion checked a e analyses. Basically, b aking was elimina ed because i mainly s ains he
on o he ame and elie es he ea .
The suppo pa e n in he compu ing model is shown in Figu e 8. The heel is clamped om one
ea slee e, which is ixed. The second ea slee e has he abili y o mo e and o a e in i s axis
(sliding), bu no pe pendicula o he axis (i ep esen s he suppo in he ea wheel). One on
slee e is le loose and he o he is loaded wi h a o ce on he leng h equal o he dis ance o he s ep
cen e. This o ce simula es he load o e ical impac , explained in Sec ion 2.3.1, wi h he ide
s anding une enly on he scoo e axis, ep esen ing he o sion. The s a ic o ce in one a m is
inc eased wi h a dynamic load ac o o 3 g o 2210 N.
Figu e 8. Heel load case wi h o ce and suppo s.
2.3.6. Ma e ial
Fo he co ec analysis se ing, i is also necessa y o know he ma e ial om which he
op imized componen will be manu ac u ed. The heel is made o 316 L s ainless s eel. The pa will
be p in ed om a omised powde supplied by he machine manu ac u e , RENISHAW. An
ad an age o he powde -p in ed pa is he imp o ed mechanical p ope ies in compa ison wi h he
same ma e ial in he o m o me allu gical p e o m p oduc s, especially Yield S eng h and Tensile
S eng h [11]. Table 1 lis s he impo an mechanical p ope ies o 316 L-p in ed ma e ial [12].
Table 1. Mechanical p ope ies o 316 L addi i ely manu ac u ed componen s.
S eel 316 L—3D P in ed Uppe Tensile S eng h (UTS)
As Buil
Ho izon al di ec ion (XY)
676 MPa ± 2 MPa
Figu e 8. Heel load case wi h o ce and suppo s.
2.3.6. Ma e ial
Fo he co ec analysis se ing, i is also necessa y o know he ma e ial om which he op imized
componen will be manu ac u ed. The heel is made o 316 L s ainless s eel. The pa will be p in ed
om a omised powde supplied by he machine manu ac u e , RENISHAW. An ad an age o he
powde -p in ed pa is he imp o ed mechanical p ope ies in compa ison wi h he same ma e ial
in he o m o me allu gical p e o m p oduc s, especially Yield S eng h and Tensile S eng h [
11
].
Table 1lis s he impo an mechanical p ope ies o 316 L-p in ed ma e ial [12].
Symme y 2020,12, 755 7 o 14
Table 1. Mechanical p ope ies o 316 L addi i ely manu ac u ed componen s.
S eel 316 L—3D P in ed Uppe Tensile S eng h (UTS) As Buil
Ho izon al di ec ion (XY) 676 MPa ±2 MPa
Ve ical di ec ion (Z) 624 MPa ±17 MPa
Yield s eng h
Ho izon al di ec ion (XY) 547 MPa ±3 MPa
Ve ical di ec ion (Z) 494 MPa ±14 MPa
Elonga ion a b eak
Ho izon al di ec ion (XY) 43% ±2%
Ve ical di ec ion (Z) 35% ±8%
Modulus o elas ici y
Ho izon al di ec ion (XY) 197 GPa ±4 GPa
Ve ical di ec ion (Z) 190 GPa ±10 GPa
Ha dness (Vicke s)
Ho izon al di ec ion (XY) 198 HV0.5 ±8 HV0.5
Ve ical di ec ion (Z) 208 HV0.5 ±6 HV0.5
Ho izon al di ec ion (XY) 4 µm o 6 µm
Ve ical di ec ion (Z) 4 µm o 6 µm
2.4. Topological Calcula ion
The opological calcula ion i sel was pe o med using he SolidThinking Inspi e (Al ai , T oy,
MI, USA) so wa e [
13
]. The so wa e uses Op iS uc sol e co e o op imiza ion. Op iS uc uses
he densi y me hod, called also he SIMP me hod (Solid Iso opic Ma e ial wi h Penalisa ion) o sol e
opological op imiza ion asks [14].
The p ocess o opological op imiza ion is ela ed o he dis ibu ion o ma e ial and he way o
joining membe s wi hin he s uc u e. Fo each elemen , he so-called “equi alen densi y” is de ined
and ea ed as a design a iable. The alue o his a iable is hen calcula ed o each elemen . A alue
o 1 is equi alen o 100% o he ma e ial and a alue o 0 is equi alen o no ma e ial. The sol e i s
a emp s o assign low s ess and equi alen densi y alue elemen s be o e analyzing he impac on
he emaining s uc u e. In his manne , he densi y o he ex aneous elemen s is close o 0, wi h he
ideal design app oaching a alue o 1. The assump ion is ha he s i ness o he ma e ial is linea ly
dependen on i s densi y. I is a designe ’s judgmen which dic a es whe e he limi is, which elemen s
should be le , and which ones omi ed. To display he “ emaining” s uc u e, an iso-plo o elemen
densi ies is used, hiding elemen s wi h a densi y below a ce ain alue, so ha an op imal design can
be seen.
The e o e, o en o ce he inal design o be exp essed by densi ies o 1 o 0 o each elemen ,
we need o use he echniques o penalize in e media e densi ies. The “powe law ep esen a ion o
elas ici y p ope ies” penaliza ion echnique is exploi ed in Op iS uc . Fo any 3D o 2D elemen i
can be exp essed as shown in Equa ion (1):
K( ) =ρpK(1)
K
and K ep esen he penalised and he eal s i ness ma ix o an elemen .
ρ
is he densi y and p
he ac o o he penalisa ion which is always g ea e han 1.
The DISCRETE pa ame e co ela es wi h (p
−
1) in Op iS uc , DISCRETE can be de ined on
he DOPTPRM bulk da a en y. A alue be ween 2.0 and 4.0 is usual o ac o p. Fo example,
i we compa e he non-penalised o mula ion (which is equi alen o p=1) a
ρ
=0.3, wi h p=2
Symme y 2020,12, 755 8 o 14
he s i ness o he elemen is educed om 0.3 o 0.09 imes he s i ness o he ully dense elemen .
Fo shell-dominan s uc u es, he de aul DISCRETE is 1.0 and o solid-dominan s uc u es is 2.0.
The dominance is de ined by he numbe o elemen s a io. DISCRT1D is an addi ional pa ame e
which can also be de ined on he DOPTPRM bulk da a en y. DISCRT1D enables 1D elemen s o use a
di e en penalisa ion o 2D o 3D elemen s [15].
The penal y s a s a 2 o he i s i e a ion, when he minimum membe size con ol is used.
Fo he second and hi d i e a ions, i inc eases o 3. This app oach p o ides a mo e disc e e solu ion.
I is clea ha when en e ing he nex i e a ion phase wi h a di e en penalisa ion ac o , he analysis
esul s may a y signi ican ly due o he exis ence o semi-dense elemen .
The me hod o opological calcula ion was se o maximize he igidi y o he s uc u e bu o
u ilize jus a de ined po ion o he incep i e olume/mass and “shape” o make he shape as s i as
possible [
16
]. The p og essi e analysis se ings we e pe o med wi h a inal elemen size o 1 mm and
a con ac se ing as a sliding only. This se ing shown in Table 2has p o en o be he mos sui able o e
se e al i e a ions [17].
Table 2. Topology analysis se ings.
Pa ame e Se Value
Analysis ype Topology op imiza ion
Objec i e Maximise s i ness
Ini ial mass a ge 30%
Elemen size 1 mm
Geome y cons ain Plane symme y (longi udinal plane)
Be o e he calcula ion, he plana symme y was se . This symme y cons ain is used o gene a e
symme ic shapes by speci ying symme y planes in he design space. In his case, he longi udinal
plane o he scoo e was used. This cons ain can be used e en unde asymme ic condi ions.
I is also necessa y o de ine “pa i ions” in he analysis. These a e places ha a e no subjec o
analysis and should emain in hei o iginal shape. Typically, hese a e di e en moun ing holes and
unc ional su aces. In he case o he heel, he pa i ions we e de ined a he poin o a achmen o he
composi e ubes, shown in Figu e 6in yellow.
The esul o he analysis is he s uc u e o he elemen s, shown in Figu e 9. The calcula ion
lea es he elemen s only whe e he load is ansmi ed [
18
]. A e he analysis, he pe cen age o he
ma e ial ep esen ed as he densi y o he elemen s can be addi ionally uned. This elemen ne wo k
se es as a suppo o subsequen modelling a e wa ds [
19
]. The ou pu om he op imiza ion
p ocess p o ide he d a design o he pa . The concep shape needs o be smoo hed and emodeled.
The co ec in e p e a ion (smoo hing) o he d a design ac ually has a huge impac on he end esul ,
especially on he weigh .
2.5. Solid Model C ea ion
The CAD model i sel is c ea ed using non-pa ame ic olume modelling based on he analysis
esul s. In he case o he heel, he ini ial o ganic model was c ea ed in SolidThinking Inspi e so wa e,
which allows PolyNURBS based modelling. I is a ee o m modelling me hod whe e a non-pa ame ic
model is o med by connec ing o ganic blocks and su aces o each o he . I is a manual way o
modelling pe o med by he designe , whe e hese geome ic elemen s a e being ex ac ed om he
opological op imiza ion esul . The o ganic shape should ace o e he op imiza ion esul p ecisely.
The elemen s a e u he shaped, in e connec ed, and o med in o a inal appea ance, as shown
in Figu e 10.
Symme y 2020,12, 755 9 o 14
Symme y 2020, 12, x FOR PEER REVIEW 8 o 14
I is clea ha when en e ing he nex i e a ion phase wi h a di e en penalisa ion ac o , he analysis
esul s may a y signi ican ly due o he exis ence o semi-dense elemen .
The me hod o opological calcula ion was se o maximize he igidi y o he s uc u e bu o
u ilize jus a de ined po ion o he incep i e olume/mass and “shape” o make he shape as s i as
possible [16]. The p og essi e analysis se ings we e pe o med wi h a inal elemen size o 1 mm and
a con ac se ing as a sliding only. This se ing shown in Table 2 has p o en o be he mos sui able
o e se e al i e a ions [17].
Be o e he calcula ion, he plana symme y was se . This symme y cons ain is used o
gene a e symme ic shapes by speci ying symme y planes in he design space. In his case, he
longi udinal plane o he scoo e was used. This cons ain can be used e en unde asymme ic
condi ions.
I is also necessa y o de ine “pa i ions” in he analysis. These a e places ha a e no subjec o
analysis and should emain in hei o iginal shape. Typically, hese a e di e en moun ing holes and
unc ional su aces. In he case o he heel, he pa i ions we e de ined a he poin o a achmen o
he composi e ubes, shown in Figu e 6 in yellow.
Table 2. Topology analysis se ings.
Pa ame e
Se Value
Analysis ype
Topology op imiza ion
Objec i e
Maximise s i ness
Ini ial mass a ge
30%
Elemen size
1 mm
Geome y cons ain
Plane symme y (longi udinal plane)
The esul o he analysis is he s uc u e o he elemen s, shown in Figu e 9. The calcula ion
lea es he elemen s only whe e he load is ansmi ed [18]. A e he analysis, he pe cen age o he
ma e ial ep esen ed as he densi y o he elemen s can be addi ionally uned. This elemen ne wo k
se es as a suppo o subsequen modelling a e wa ds [19]. The ou pu om he op imiza ion
p ocess p o ide he d a design o he pa . The concep shape needs o be smoo hed and emodeled.
The co ec in e p e a ion (smoo hing) o he d a design ac ually has a huge impac on he end
esul , especially on he weigh .
Figu e 9. Topology analysis esul .
2.5. Solid Model C ea ion
The CAD model i sel is c ea ed using non-pa ame ic olume modelling based on he analysis
esul s. In he case o he heel, he ini ial o ganic model was c ea ed in SolidThinking Inspi e so wa e,
which allows PolyNURBS based modelling. I is a ee o m modelling me hod whe e a non-
Figu e 9. Topology analysis esul .
Symme y 2020, 12, x FOR PEER REVIEW 9 o 14
pa ame ic model is o med by connec ing o ganic blocks and su aces o each o he . I is a manual
way o modelling pe o med by he designe , whe e hese geome ic elemen s a e being ex ac ed
om he opological op imiza ion esul . The o ganic shape should ace o e he op imiza ion esul
p ecisely. The elemen s a e u he shaped, in e connec ed, and o med in o a inal appea ance, as
shown in Figu e 10.
Figu e 10. PolyNURBS CAD model.
One i e a ion o he ea heel conside ed was he shell pa , whe e u he ligh ening would
occu . Mo eo e , he solid model c ea ed abo e would be pa ially hollowed in hick a eas. I was a
epe i i e p ocess o inding he ideal wall hickness, which was always e i ied by an FEM analysis.
Ul ima ely, he su icien hickness o he wall was ound o be 1.3 mm. Shell modelling was
pe o med using Au odesk In en o so wa e by su ace modelling.
Howe e , his shell heel pa shown in Figu e 11 was no used on he ame. I would be
echnologically di icul o emo e unbaked powde om he ca i ies ( equi ing d illing holes). The
weigh educ ion was minimal, bu he maximum on Mises s ess inc eased.
Figu e 11. Shell a ian .
2.6. FEM Analysis
The FEM analysis se ed bo h o alida e he indi idual s eps du ing he design and o inal
check he s i ness and s eng h o he ame pa . The analysis was also pe o med in SolidThinking
Inspi e so wa e.
Inspi e c ea es and uses mesh du ing op imiza ion as well du ing analysis. Meshing se up and
c ea ion happens in an au oma ed meshing s ep in he backg ound using a powe ul algo i hm o
calcula e mesh size. Inspi e uses a combina ion o Hype Mesh and Simlab o meshing—bo h could
Figu e 10. PolyNURBS CAD model.
One i e a ion o he ea heel conside ed was he shell pa , whe e u he ligh ening would occu .
Mo eo e , he solid model c ea ed abo e would be pa ially hollowed in hick a eas. I was a epe i i e
p ocess o inding he ideal wall hickness, which was always e i ied by an FEM analysis. Ul ima ely,
he su icien hickness o he wall was ound o be 1.3 mm. Shell modelling was pe o med using
Au odesk In en o so wa e by su ace modelling.
Howe e , his shell heel pa shown in Figu e 11 was no used on he ame. I would be
echnologically di icul o emo e unbaked powde om he ca i ies ( equi ing d illing holes).
The weigh educ ion was minimal, bu he maximum on Mises s ess inc eased.
2.6. FEM Analysis
The FEM analysis se ed bo h o alida e he indi idual s eps du ing he design and o inal
check he s i ness and s eng h o he ame pa . The analysis was also pe o med in SolidThinking
Inspi e so wa e.
Inspi e c ea es and uses mesh du ing op imiza ion as well du ing analysis. Meshing se up and
c ea ion happens in an au oma ed meshing s ep in he backg ound using a powe ul algo i hm o
calcula e mesh size. Inspi e uses a combina ion o Hype Mesh and Simlab o meshing—bo h could
be conside ed he bes meshing ools. I needed, a use can ake con ol o mesh sizes o di e en
componen s, bu usually, he de aul mesh size gi es he bes esul s. The inal analysis was pe o med