failure of two overhead crane shafts - srce
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– En
gine
erin
g Po
wer
Željk
o D
omaz
et1 ,
Fran
cisk
o Lu
kša1 ,
Miro
Bug
arin
1
Failu
re o
f tw
o ov
erhe
ad c
rane
sha
fts
1 Fac
ulty
of E
lect
rical
Eng
inee
ring,
Mec
hani
cal E
ngin
eerin
g an
d N
aval
Arc
hite
ctur
e; U
nive
rsity
of S
plit;
Spl
it, C
roat
ia
Abs
trac
t
The
failu
re a
naly
sis
of tw
o ov
erhe
ad c
rane
sha
fts is
pre
sent
ed: t
he fa
ilure
of a
n ov
erhe
ad c
rane
dri
ve s
haft
and
the
failu
re o
f an
over
head
cra
ne g
earb
ox sh
aft,
due
to ro
tatin
g-be
ndin
g fa
tigue
. The
frac
ture
of t
he o
verh
ead
cran
e dr
ive
shaf
t ori
gina
ted
in s
mal
l rad
ius
fille
t bet
wee
n tw
o di
ffere
nt d
iam
eter
s of
the
shaf
t. A
new
sha
ft w
as m
ade
with
a
larg
er-s
ize
fille
t, re
sulti
ng in
redu
ced
stre
ss c
once
ntra
tion
in th
is re
gion
. The
failu
re o
f the
ove
rhea
d cr
ane
gear
box
shaf
t ori
gina
ted
in th
e in
ters
ectio
n of
two
stre
ss r
aise
rs, d
ue to
a c
hang
e in
the
shaf
t dia
met
er a
nd in
the
keyw
ay
corn
er. A
new
shaf
t was
mad
e w
ith a
larg
er-s
ize
fille
t and
a la
rger
size
radi
us o
f the
key
way
cor
ner t
o m
inim
ize
stre
ss
conc
entr
atio
n in
this
sect
ion.
In b
oth
case
s the
inst
alle
d co
uplin
gs w
ere
repl
aced
by
gear
cou
plin
gs in
ord
er to
allo
w
para
llel a
nd a
ngul
ar m
isal
ignm
ent a
s w
ell a
s to
avo
id a
dditi
onal
load
due
to m
isal
ignm
ent.
The
anal
ysis
sho
ws
that
th
e fa
tigue
life
can
be
sign
ifica
ntly
incr
ease
d w
ith a
sim
ple
chan
ge in
the
stru
ctur
al d
etai
ls
Key
wor
ds: F
ailu
re a
naly
sis;
Sha
ft fa
ilure
s; O
verh
ead
cran
es
1. I
ntro
duct
ion
The
fatig
ue f
ract
ures
of
shaf
ts o
rigin
ate
at p
oint
s of
st
ress
con
cent
ratio
n, s
uch
as c
hang
es in
the
shaf
t dia
m-
eter
and
end
s of
the
keyw
ays.
The
shar
p co
rner
at t
he
inte
rsec
tion
betw
een
two
diffe
rent
dia
met
ers o
f the
shaf
ts
or in
the
botto
m o
f the
key
way
can
cau
se lo
cal s
tress
to
be fe
w ti
mes
gre
ater
than
the a
vera
ge n
omin
al st
ress
. The
fa
ilure
ana
lysi
s of
an
over
head
cra
ne tr
olle
y dr
ive
shaf
t is
pre
sent
ed i
n th
e fir
st p
art
of t
his
pape
r. Th
e fa
ilure
or
igin
ated
in th
e ra
dius
fill
et b
etw
een
two
diffe
rent
di-
amet
ers o
f the
shaf
t. Th
e fa
ilure
ana
lysi
s of a
n ov
erhe
ad
cran
e tro
lley
gear
box
shaf
t is
pre
sent
ed i
n th
e se
cond
pa
rt of
the
pape
r. Th
e fa
ilure
of
this
sha
ft or
igin
ated
at
the
inte
rsec
tion
of tw
o st
ress
rai
sers
, the
cha
nge
in th
e sh
aft d
iam
eter
and
key
way
.
2. F
ailu
re o
f ove
rhea
d cr
ane
driv
e sh
aft
In “
Stee
lwor
ks S
plit”
the
high
-spe
ed e
lect
ric o
verh
ead
cran
e, F
ig.1
, was
suita
ble
for t
rans
port
of th
e bill
ets f
rom
th
e m
elt
shop
to
the
rolli
ng m
ill h
all.
The
cran
e w
as
rate
d at
10
tons
with
a sp
an o
f 20.
5 m
and
han
dled
abo
ut
100
lifts
and
tra
nspo
rts p
er d
ay,
each
lift
ave
ragi
ng 5
to
ns. T
he st
eppe
d dr
ive
shaf
t use
d fo
r an
over
head
cra
ne
trolle
y w
heel
fra
ctur
ed a
fter
24 m
onth
s of
ser
vice
. The
el
ectri
c m
otor
pow
er r
atin
g w
as 3
kW
with
an
outp
ut
spee
d of
940
rpm
. The
max
imum
tra
vel
spee
d of
the
tro
lley
was
32
m/m
in.
The
shaf
t w
as c
onne
cted
with
the
gea
rbox
by
a ro
ller
chai
n co
uplin
g, s
uppo
rted
by t
wo
rolle
r be
arin
gs a
nd
conn
ecte
d w
ith th
e w
heel
by
a ke
y, F
igur
e 2.
The
shaf
t w
as m
ade
of q
uenc
hed
and
tem
pere
d st
eel
25C
rMo4
acco
rdin
g to
Ger
man
stan
dard
DIN
(Deu
tsch
es
Inst
itut f
ür N
orm
ung)
[1].
The
chem
ical
com
posi
tion
of
mat
eria
l was
ver
ified
by
usin
g qu
anto
met
er. T
he h
ard-
ness
and
the
mic
rost
ruct
ure
wer
e co
nfirm
ed to
be
tem
-pe
red
stee
l 25C
rMo4
. The
frac
ture
occ
urre
d on
the
fille
t
Fig.
1. O
verh
ead
cran
e fo
r tra
nspo
rt of
bill
ets
Fig.
2. O
verh
ead
cran
e tro
lley
[2]
Vol.
15(1
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–
15
due
to c
hang
e be
twee
n tw
o di
ffere
nt d
iam
eter
s of
the
sh
aft
appr
oxim
atel
y 22
5 m
m f
rom
the
driv
en e
nd a
nd
appr
oxim
atel
y 30
mm
fro
m o
ne e
nd o
f th
e ke
yway
w
here
the
cran
e w
heel
was
key
ed to
the
axle
, Fig
ure
3.
2.1.
Fra
ctur
e su
rfac
e in
vest
igat
ion
The
cont
our o
f the
frac
ture
sur
face
was
con
vex
with
re-
spec
t to
the
smal
ler-s
ectio
n si
de. T
here
wer
e th
ree
frac
-tu
re re
gion
s, Fi
gure
4: a
regi
on o
f mul
tiple
cra
ck o
rigin
s ar
ound
the
oute
r per
imet
er (a
t A);
a re
gion
of t
he c
rack
pr
opag
atio
n zo
ne (
at B
); an
d a
regi
on o
f th
e fin
al, f
ast
frac
ture
(at C
).
The p
rese
nce o
f mul
tiple
crac
k or
igin
s sep
arat
ed b
y ra
tche
t m
arks
aro
und
the
oute
r per
imet
er w
as a
n in
dica
tion
of ro
-ta
tiona
l-ben
ding
fatig
ue w
ith se
vere
stre
ss c
once
ntra
tion.
The
rela
tivel
y sm
all s
ize
of th
e fin
al fr
actu
re re
gion
was
an
indi
catio
n of
low
nom
inal
stre
ss. I
n ro
tatio
nal-b
end-
ing,
dur
ing
each
revo
lutio
n, e
very
poi
nt o
f the
sha
ft ci
r-cu
mfe
renc
e w
as s
ubje
cted
to te
nsile
-com
pres
sive
stre
ss
and
ther
efor
e th
e cr
ack
coul
d be
initi
ated
at a
ny p
oint
on
the
shaf
t per
iphe
ry.
The
indi
vidu
al c
rack
s pr
opag
ated
tow
ard
a sin
gle
crac
k fro
nt, r
egio
n B,
Fig
ure
4. T
he c
rack
surfa
ces w
ere
pres
sed
toge
ther
dur
ing
the
com
pres
sive
com
pone
nt o
f the
stre
ss
cycl
e, a
nd m
utua
l ru
bbin
g oc
curre
d. T
he b
each
mar
ks
wer
e not
visi
ble b
ecau
se th
ey w
ere o
blite
rate
d by
rubb
ing.
The
conc
lusi
on f
rom
the
surf
ace
inve
stig
atio
n w
as th
at
the
shaf
t fra
ctur
ed a
s a
resu
lt of
rot
atio
nal-b
endi
ng f
a-
tigue
. The
prim
ary
caus
e of
the
frac
ture
was
the
bend
ing
load
dur
ing
the
rota
tion,
alth
ough
the
tota
l loa
d w
as a
co
mbi
natio
n of
ben
ding
and
tors
iona
l loa
ds. T
he s
mal
l ra
dius
of t
he fi
llet a
t a c
hang
e in
shaf
t dia
met
er, d
etai
l B
in F
igur
e 3,
resu
lted
in h
igh
stre
ss c
once
ntra
tion,
whi
ch
initi
ated
the
crac
k.
The
visu
al e
xam
inat
ion
of th
e w
heel
and
rai
l rev
eale
d sm
ooth
and
ligh
t con
tact
are
a on
the
side
s of
bot
h pa
rts
due
to m
utua
l ru
bbin
g, d
etai
l in
Fig
ure
1, w
hich
was
ca
used
by
addi
tiona
l tor
sion
al lo
ad. P
ost-f
ailu
re v
erifi
-ca
tion
of p
aral
lelis
m a
nd s
traig
htne
ss o
f th
e ra
ils w
ith
optic
al in
stru
men
t rev
eale
d m
isal
ignm
ent i
n pa
ralle
lism
an
d st
raig
htne
ss.
2.2.
Str
ess
anal
ysis
2.2.
1. B
endi
ng s
tress
es
Dur
ing
norm
al o
pera
tion,
ben
ding
stre
sses
in th
e cr
itica
l ar
ea w
ere
caus
ed b
y a
whe
el v
ertic
al l
oad.
The
whe
el
verti
cal
load
was
con
side
red
as a
for
ce a
pplie
d at
the
ce
nter
line
of t
he w
heel
con
tact
with
the
shaf
t, se
e Fi
gure
5.
The
appl
ied
forc
e was
calc
ulat
ed fr
om th
e des
ign
load
, se
e re
fere
nce
[2].
A n
umer
ical
ana
lysi
s of
loca
l stre
sses
was
don
e by
the
finite
ele
men
t met
hod
usin
g A
DIN
A s
oftw
are.
The
line
-ar
ela
stic
mod
el w
ith 3
D so
lid e
lem
ents
with
eig
ht D
OF
per n
odes
was
use
d, F
igur
e 5.
Eac
h no
de h
ad 3
deg
rees
of
free
dom
, tra
nsla
tion
in X
, Y an
d Z
dire
ctio
n. T
he m
od-
el is
fixe
d in
the
line
on th
e po
sitio
ns o
f bea
ring
cent
ers
and
load
ed w
ith c
once
ntra
ted
forc
es in
the
node
s. Th
e nu
mer
ical
ana
lysi
s of
loca
l stre
sses
reve
aled
that
des
ign
forc
e du
e to
ver
tical
load
sho
uld
not h
ave
led
to s
haft
frac
ture
. For
ce 3
0 kN
cau
sed
loca
l stre
sses
of 7
9 M
Pa in
th
e cr
itica
l are
a.
Post
-fai
lure
ver
ifica
tion
reve
aled
par
alle
l mis
alig
nmen
t of
0.5
mm
bet
wee
n tw
o sh
aft a
xes.
The
num
eric
al a
nal-
ysis
of
loca
l stre
sses
rev
eale
d th
at d
ispl
acem
ent o
f 0.
5 m
m c
ause
d an
inc
reas
e in
loc
al s
tress
es i
n th
e cr
itica
l ar
ea th
ree
times
(298
MPa
), Fi
gure
5.
A ro
ller c
hain
cou
plin
g w
as u
sed
to tr
ansm
it po
wer
be-
twee
n sh
afts
. The
torq
ue w
as tr
ansm
itted
thro
ugh
a do
u-bl
e ro
ller c
hain
. Due
to c
lear
ance
s bet
wee
n th
e ch
ain
and
the
spro
cket
tee
th o
n tw
o co
uplin
gs,
the
rolle
r ch
ain
coup
ling
perm
itted
ecc
entri
city
– ε
(pa
ralle
l m
isal
ign-
men
t) be
twee
n sh
afts
up
to 2
% o
f the
rolle
r cha
in p
itch
Fig.
3. S
tepp
ed d
rive
shaf
t
Fig.
4. F
ract
ure
surf
aces
Fig.
5. N
umer
ical
ana
lysi
s
16
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––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
– En
gine
erin
g Po
wer
and
angu
lar
mis
alig
nmen
t – α
bet
wee
n sh
afts
up
to 1
°, [3
], se
e Fi
gure
6.
If e
ccen
trici
ty a
nd a
ngul
ar m
isal
ignm
ent
betw
een
the
whe
el s
haft
axis
and
the
driv
e ax
is i
s hi
gher
tha
n th
e ch
ain
coup
ling
can
com
pens
ate,
ther
e is
a v
ertic
al fo
rce
on t
he e
nd o
f th
e w
heel
sha
ft an
d al
so c
orre
spon
ding
ad
ditio
nal b
endi
ng s
tress
es in
the
criti
cal p
lace
.
2.2.
2. T
orsi
onal
stre
sses
The
max
imum
app
lied
torq
ue o
f 71
6 N
m i
n th
e dr
ive
shaf
t was
est
imat
ed fr
om th
e el
ectri
c m
otor
pow
er ra
ting
of 3
kW
, the
max
imum
trav
el s
peed
of t
he tr
olle
y of
32
m/m
in a
nd th
e w
heel
dia
met
er w
as 2
50 m
m. T
he c
alcu
-la
ted
nom
inal
she
ar s
tress
for
the
shaf
t dia
met
er o
f 50
m
m w
as 2
8.6
MPa
. The
stre
ss c
once
ntra
tion
fact
or d
ue
to to
rsio
nal s
tress
at a
cha
nge
of th
e sh
aft d
iam
eter
ac-
cord
ing
to l
itera
ture
[4]
was
1.8
. The
max
imum
she
ar
loca
l stre
ss a
t the
inte
rsec
tion
of th
e ch
ange
of t
he s
haft
diam
eter
due
to s
tress
con
cent
ratio
n w
as 5
1.5
MPa
.
From
the
com
paris
on b
etw
een
bend
ing
and
shea
r stre
ss-
es it
was
con
clud
ed th
at b
endi
ng st
ress
es w
ere
dom
inan
t fo
r the
sha
ft fr
actu
re.
2.3.
Cor
rect
ive
actio
n
A c
orre
ctiv
e ac
tion
was
con
side
red
in tw
o w
ays:
a) D
ecre
asin
g th
e st
ress
con
cent
ratio
n in
the
criti
cal a
rea
by in
crea
sing
the
size
of t
he fi
llet r
adiu
s an
d
b) R
educ
ing
the
influ
ence
of
para
llel m
isal
ignm
ent b
e-tw
een
the
shaf
t axi
s an
d co
uplin
g ax
is o
n lo
cal s
tress
es
by c
hang
ing
the
type
of
the
coup
ling,
whi
ch p
erm
itted
m
ore
para
llel m
isal
ignm
ent b
etw
een
axes
.
2.3.
1. In
crea
sing
the
size
of t
he fi
llet r
adiu
s
The
dist
ance
bet
wee
n th
e la
rge
diam
eter
of
the
shaf
t (w
heel
) and
the
bear
ing
was
11
mm
, Fig
ure
7. T
he sp
ac-
er w
as p
ositi
oned
bet
wee
n th
e w
heel
and
bea
ring.
In-
crea
sing
the
size
of
the
fille
t rad
ius
was
lim
ited
by th
e de
sign
of t
he s
pace
r.
Ther
efor
e, n
umer
ical
exp
erim
ents
wer
e ca
rrie
d ou
t fo
r fo
ur d
iffer
ent s
izes
of t
he fi
llet r
adiu
s in
ord
er to
redu
ce
loca
l stre
sses
bel
ow th
e en
dura
nce
limit,
Fig
ures
8 a
nd
10.
Fig.
6. R
olle
r cha
in c
oupl
ing
[3]
Fig.
7. D
esig
n of
the
spac
er
Fig.
8. S
tress
dis
tribu
tion
Fig.
9. G
ear c
oupl
ing,
[7]
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––––
––––
––––
––––
––––
–
17
The
stre
ss c
once
ntra
tion
fact
ors
in th
e cr
itica
l are
as h
ad
a go
od a
gree
men
t with
lite
ratu
re [4
] and
[5].
The
fatig
ue
stre
ngth
cur
ve o
f th
e m
ater
ial w
as u
sed
from
lite
ratu
re
[6].
The
curv
es in
Fig
ure
8 sh
ow th
e in
crea
sing
siz
e of
the
fille
t rad
ius
from
1.5
mm
to 5
mm
, red
ucin
g m
axim
um
loca
l stre
ss b
y ab
out 1
.5 ti
mes
(fro
m 2
98 to
200
MPa
).
2.3.
2. C
hang
e of
the
coup
ling
type
A g
ear
coup
ling
was
con
side
red
to s
ubst
itute
the
rolle
r ch
ain
coup
ling,
Fig
ure
9. T
he g
ear c
oupl
ing
can
acco
m-
mod
ate m
ore e
ccen
trici
ty an
d an
gula
r mis
alig
nmen
t tha
n th
e ro
ller c
hain
cou
plin
g. A
ccor
ding
to [7
], th
e ge
ar c
ou-
plin
g pe
rmits
par
alle
l of
fset
0.7
5 m
m,
angu
lar
3° a
nd
axia
l gap
from
-0.5
to 1
mm
. Sin
ce p
ost-f
ailu
re v
erifi
ca-
tion
reve
aled
par
alle
l mis
alig
nmen
t of 0
.5 m
m b
etw
een
two
shaf
t axe
s, th
e ap
plic
atio
n of
the
gear
cou
plin
g in
th
is ca
se ca
n el
imin
ate f
orce
on
the s
haft
due t
o m
isal
ign-
men
t an
d ca
n al
so r
educ
e lo
cal
stre
sses
in
the
criti
cal
area
.
Figu
re 1
0 sh
ows
the
influ
ence
of
cons
ider
ed c
orre
ctiv
e ac
tions
on
fatig
ue li
fe.
The
actu
al s
ervi
ce li
fe w
as e
stim
ated
from
the
wor
king
tim
e of
the
cran
e, th
e nu
mbe
r of
lifti
ngs
and
the
whe
el
diam
eter
. The
cra
ne w
as in
ser
vice
for a
bout
400
wor
k-in
g da
ys in
the
perio
d of
two
year
s. Th
e av
erag
e nu
mbe
r of
tran
spor
ts p
er d
ay w
as 1
00 w
ith th
e tra
vel o
f the
trol
-le
y 10
m p
er e
ach
trans
port.
For
the
whe
el d
iam
eter
of
250
mm
and
the
corr
espo
ndin
g sh
aft t
he a
ctua
l ser
vice
lif
e w
as a
bout
4.8
·105 c
ycle
s. Th
e es
timat
ed s
ervi
ce li
fe
from
the n
umer
ical
mod
el w
as ab
out 3
·105 c
ycle
s, Fi
gure
10
.
The
rede
sign
of t
he s
haft
fille
t rad
ius
from
1.5
mm
to 5
m
m r
educ
ed m
axim
um l
ocal
stre
ss b
elow
the
fat
igue
en
dura
nce
limit
(abo
ut 9
0% o
f en
dura
nce
limit)
. Th
e ap
plic
atio
n of
a g
ear c
oupl
ing
to a
ccom
mod
ate
para
llel
mis
alig
nmen
t re
duce
d m
axim
um l
ocal
stre
ss t
o ab
out
35%
of
the
endu
ranc
e lim
it, w
hat
was
mor
e th
an t
wo
times
in
com
paris
on t
o th
e re
desi
gn o
f th
e sh
aft
fille
t ra
dius
. A c
ombi
natio
n of
the
fille
t rad
ius
rede
sign
and
th
e ap
plic
atio
n of
the
gear
cou
plin
g ad
ditio
nally
redu
ced
loca
l stre
sses
, Fig
ure
10.
Bas
ed o
n th
is a
naly
sis,
the
actu
al se
rvic
e lif
e of
the
shaf
t ca
n be
impr
oved
fro
m th
e fin
ite (
abou
t 4.8
·105 c
ycle
s)
to th
e in
finite
life
time.
2.3.
3. C
orre
ctio
n
New
sha
fts w
ere
mad
e fr
om q
uenc
hed
and
tem
pere
d st
eel 4
2CrM
o4 a
ccor
ding
to D
IN [
1] w
ith a
larg
er-s
ize
fille
t, w
hich
min
imiz
ed s
tress
con
cent
ratio
n in
this
re-
gion
and
pre
vent
ed re
curr
ence
of t
he fa
ilure
. The
rolle
r ch
ain
coup
lings
wer
e re
plac
ed b
y ge
ar c
oupl
ings
to r
e-du
ce th
e in
fluen
ce o
f par
alle
l mis
alig
nmen
t bet
wee
n th
e sh
aft a
xis
and
coup
ling
axis
on
loca
l stre
sses
.
3. F
ailu
re o
f ove
rhea
d cr
ane
gear
box
shaf
t
An
elec
tric
over
head
cra
ne, F
ig. 1
1, w
as s
uita
ble
for t
he
trans
port
of a
ladl
e with
liqu
id st
eel f
rom
the l
adle
furn
ace
to th
e co
ntin
uous
cas
ting
mac
hine
. The
cra
ne w
as ra
ted
at
50 to
ns w
ith a
spa
n of
18.
4 m
and
han
dled
abo
ut 2
0 lif
ts an
d tra
nspo
rts p
er d
ay, e
ach
lift a
vera
ging
43
tons
. The
ste
pped
driv
e sha
ft us
ed in
an o
verh
ead
cran
e tro
lley
gear
-bo
x, F
igur
e 12
, bro
ke a
fter 3
6 m
onth
s of
ser
vice
.
The
elec
tric
mot
or p
ower
rat
ing
was
5.5
kW
with
an
outp
ut s
peed
of 9
40 rp
m. T
he m
axim
um tr
avel
spe
ed o
f th
e tro
lley
was
20
m/m
in. T
he o
verh
ead
cran
e tro
lley
gear
box
[8] i
s sho
wn
in F
igur
e 12
and
the
shaf
t is s
how
n in
Fig
ures
13
and
14.
Fig.
10.
Influ
ence
of c
orre
ctiv
e ac
tions
on
fatig
ue li
fe
Fig.
11.
Ove
rhea
d cr
ane
for t
rans
port
of la
dle
with
liqu
id s
teel
Fig.
12.
Ove
rhea
d cr
ane
trolle
y ge
arbo
x
18
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
– En
gine
erin
g Po
wer
3.1.
Fra
ctur
e su
rfac
e in
vest
igat
ion
The
shaf
t was
mad
e of
con
stru
ctio
n st
eel S
t 52-
3 ac
cord
-in
g to
DIN
[9].
The
frac
ture
occ
urre
d on
a fi
llet d
ue to
ch
ange
bet
wee
n tw
o di
ffere
nt d
iam
eter
s of
the
shaf
t ap-
prox
imat
ely
110
mm
from
one
end
. The
con
tour
of t
he
frac
ture
sur
face
was
con
vex
with
res
pect
to th
e sm
all-
er-s
ectio
n si
de.
Ther
e w
ere
four
fra
ctur
e re
gion
s, Fi
gure
15.
Num
erou
s ra
tche
t mar
ks (a
t A),
on th
e ou
ter e
dge
of th
e su
rface
and
th
e da
rk b
and
at th
is ed
ge in
dica
te f
atig
ue c
rack
s in
itia-
tion,
wha
t is a
cha
ract
erist
ic o
f rot
atio
nal-b
endi
ng fa
tigue
. Tw
o cr
acks
(at
B)
from
the
key
way
cor
ners
sug
geste
d to
rsio
nal s
tress
es. T
he cr
acks
prop
agat
ed ci
rcum
fere
ntia
lly
arou
nd th
e sh
aft (
at C
). Th
e fin
al f
ract
ure
was
a m
ixed
du
ctile
and
brit
tle fr
actu
re in
the
mid
dle
of th
e el
liptic
al
cont
our (
at D
). Th
e be
ach
mar
ks w
ere
not v
isibl
e be
caus
e th
ey w
ere
oblit
erat
ed b
y ru
bbin
g.
In th
is ca
se th
ere w
ere t
wo
stre
ss ra
iser
s in
the s
ame a
rea:
a
shar
p co
rner
in th
e ke
yway
and
a c
hang
e in
the
shaf
t di
amet
er. A
dditi
onal
ly, t
he e
nd o
f th
e ke
yway
was
due
to
chan
ge in
the s
haft
diam
eter
, fra
ctur
e sec
tion
in F
igur
e 13
, cau
sing
hig
h co
ncen
tratio
n of
stre
sses
.
The c
oncl
usio
n fro
m th
e sur
face
inve
stiga
tion
was
that
the
shaf
t fra
ctur
ed as
a re
sult
of th
e rot
atio
nal-b
endi
ng fa
tigue
du
e to
high
stre
ss co
ncen
tratio
n. T
he cr
acks
wer
e ini
tiate
d
in th
e int
erse
ctio
n of
two
stres
s rai
sers
, on
the s
harp
corn
er
in th
e ke
yway
and
on
the
radi
us o
f the
fille
t due
to c
hang
e in
the
shaf
t dia
met
er, d
etai
l B in
Fig
ure
13.
3.2.
Str
ess
anal
ysis
3.2.
1. B
endi
ng s
tress
es
A s
plit
muf
f co
uplin
g w
as u
sed
to t
rans
mit
pow
er b
e-tw
een
the
shaf
ts, F
ig.1
2.
The
split
muf
f co
uplin
g is
a ty
pe o
f rig
id c
oupl
ing
and
shou
ld b
e us
ed w
hen
the
alig
nmen
t of t
he tw
o sh
afts
can
be
mai
ntai
ned
very
acc
urat
ely.
A s
mal
l m
issa
lignm
ent
betw
een
two
shaf
ts c
an c
ause
hig
h st
ress
es. P
ost-f
ailu
re
verif
icat
ion
reve
aled
par
alle
l m
isal
ignm
ent
of 0
.8 m
m
betw
een
the
gear
box
shaf
t axi
s an
d th
e dr
ive
shaf
t axi
s of
the
whe
el, F
igur
e 16
.
The
num
eric
al a
naly
sis o
f loc
al st
ress
es w
as d
one
by th
e fin
ite e
lem
ent m
etho
d us
ing
AD
INA
sof
twar
e. T
he a
p-pl
ied
forc
e of
F=1
5000
N w
as e
stim
ated
from
the
para
l-le
l mis
alig
nmen
t of
d=0.
8 m
m a
ccor
ding
to e
xpre
ssio
n (1
), Fi
gure
17,
whe
re l
= 7
20 m
m a
nd a
= 1
80 m
m,
Figu
re 1
6.
Fig.
13.
Ste
pped
driv
e sh
aft [
8]
Fig.
14.
Ste
pped
driv
e br
oken
sha
ft
Fig.
15.
Fra
ctur
e su
rfac
es
Fig.
16.
Mis
alig
nmen
t bet
wee
n th
e ge
arbo
x sh
aft a
xis
and
driv
e sh
aft a
xis
of th
e w
heel
Fig.
17.
Def
lect
ion
Vol.
15(1
) 202
0 ––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
–
19
d
Fa EIla
=−
()
2
63�
(1
)
The
linea
r el
astic
mod
el w
ith 3
D s
olid
ele
men
ts w
ith
eigh
t DO
F pe
r nod
es w
as u
sed,
Fig
ure 1
8. E
ach
node
had
3
degr
ees o
f fre
edom
, tra
nsla
tion
in X
, Y a
nd Z
dire
ctio
n.
The
mod
el is
fixe
d in
the
back
side
face
and
load
ed w
ith
conc
entra
ted
forc
es in
the
node
on
the
front
sid
e.
The
FEM
ana
lysi
s of
loc
al s
tress
es r
evea
led
that
the
m
axim
um st
ress
217
MPa
was
in th
e sh
arp
corn
er o
f the
ke
yway
and
the
stre
ss o
n th
e fil
let d
ue to
cha
nge
in th
e sh
aft d
iam
eter
nea
r the
key
way
was
154
MPa
, Fig
ure
18.
Stre
ss c
once
ntra
tion
fact
ors
in c
ritic
al a
reas
had
a g
ood
agre
emen
t with
lite
ratu
re [4
] and
[5].
3.2.
2. T
orsi
onal
stre
sses
The m
axim
um ap
plie
d to
rque
of 1
458
Nm
in th
e gea
rbox
ou
tput
shaf
t was
est
imat
ed fr
om th
e el
ectri
c m
otor
pow
-er
ratin
g of
5.5
kW
with
an
outp
ut sp
eed
of 9
40 rp
m a
nd
the
gear
box
trans
mis
sion
ratio
26.
The
cal
cula
ted
shea
r st
ress
for
the
shaf
t dia
met
er o
f 65
mm
was
26.
5 M
Pa.
The s
tress
conc
entra
tion
fact
or d
ue to
tors
iona
l stre
ss d
ue
to c
hang
e of
the
shaf
t dia
met
er w
as 1
.5 a
nd d
ue to
the
keyw
ay it
was
1.7
[4].
The
max
imum
loca
l stre
ss d
ue to
ch
ange
in th
e sha
ft di
amet
er an
d th
e key
way
due
to st
ress
co
ncen
tratio
n w
as 6
7.6
MPa
.
3.3.
Cor
rect
ive
actio
n
Cor
rect
ive
actio
n w
ere
cons
ider
ed in
bot
h cr
itica
l are
as:
a) In
crea
sing
the
fille
t rad
ius
due
to c
hang
e in
the
shaf
t di
amet
er fr
om 2
.5 m
m to
4 m
m, F
ig. 1
9.
b) In
crea
sing
the r
adiu
s in
the k
eyw
ay co
rner
of t
he m
ax-
imum
siz
e. T
he m
axim
um r
adiu
s si
ze i
n th
e ke
yway
co
rner
for
the
shaf
t dia
met
er 6
5 m
m a
ccor
ding
to D
IN
[10]
was
0.6
mm
, Fig
. 19.
c) R
educ
ing
the
influ
ence
of
para
llel m
isal
ignm
ent b
e-tw
een
the
shaf
t axi
s an
d co
uplin
g ax
is o
n lo
cal s
tress
es
by c
hang
ing
the
type
of c
oupl
ing
whi
ch p
erm
its p
aral
lel
mis
alig
nmen
t bet
wee
n ax
es.
3.3.
1. In
crea
sing
bot
h th
e ra
dius
in th
e ke
yway
co
rner
and
the
radi
us d
ue to
cha
nge
in th
e sh
aft d
iam
eter
.
The
FEM
ana
lysis
of
loca
l stre
sses
afte
r th
e re
desig
n re
-ve
aled
dec
reas
ing
the m
axim
um b
endi
ng st
ress
in th
e sha
rp
corn
er o
f the
key
way
from
217
MPa
to 1
45 M
Pa a
s w
ell
as d
ecre
asin
g str
esse
s of
the
fille
t rad
ius
due
to c
hang
e in
th
e sh
aft d
iam
eter
from
154
MPa
to 8
6 M
Pa, F
igur
e 20
.
Fig.
18.
Num
eric
al a
naly
sis
Fig.
19.
Orig
inal
and
impr
oved
des
ign
of th
e fil
let r
adiu
s
Fig.
20.
Num
eric
al a
naly
sis
20
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
––––
– En
gine
erin
g Po
wer
3.3.
2. C
hang
e of
the
coup
ling
type
A g
ear
coup
ling
was
con
side
red
to s
ubst
itute
the
spl
it m
uff
coup
ling
sinc
e po
st-f
ailu
re v
erifi
catio
n re
veal
ed
para
llel m
isal
ignm
ent o
f 0,8
mm
bet
wee
n tw
o sh
aft a
xes.
The
appl
icat
ion
of g
ear c
oupl
ings
can
elim
inat
e fo
rce
on
the
shaf
t due
to m
isal
ignm
ent a
nd c
an a
lso
redu
ce lo
cal
stre
sses
on
the
criti
cal a
rea.
Figu
re 2
1 sh
ows
the
influ
ence
of
cons
ider
ed c
orre
ctiv
e ac
tions
on
the
fatig
ue li
fe. T
he fa
tigue
stre
ngth
cur
ve o
f th
e m
ater
ial i
s us
ed fr
om li
tera
ture
[11]
.
The
actu
al s
ervi
ce li
fe w
as e
stim
ated
from
the
wor
king
tim
e of
the
cran
e, th
e nu
mbe
r of
lifti
ngs
and
the
whe
el
diam
eter
. The
cra
ne w
as in
ser
vice
for a
bout
800
wor
k-in
g da
ys d
urin
g a
thre
e ye
ar p
erio
d. T
he a
vera
ge n
umbe
r of
tran
spor
ts p
er d
ay w
as 2
0 w
ith th
e tra
vel o
f the
trol
ley
12 m
per
eac
h tra
nspo
rt. F
or th
e w
heel
dia
met
er o
f 630
m
m a
nd th
e co
rres
pond
ing
shaf
t, th
e ac
tual
ser
vice
life
w
as 3
.5·1
05 cyc
les.
The
estim
ated
ser
vice
life
fro
m th
e nu
mer
ical
mod
el w
as a
bout
3·1
05 cyc
les,
Figu
re 1
0.
The
rede
sign
of th
e sh
aft f
illet
radi
us re
duce
d th
e m
axi-
mum
loca
l stre
ss a
nd th
e es
timat
ed fa
tigue
life
was
abo
ut
two
times
long
er a
ccor
ding
to a
ctua
l fat
igue
life
, Fig
ure
21. T
he a
pplic
atio
n of
a g
ear
coup
ling
to a
ccom
mod
ate
para
llel m
isalig
nmen
t elim
inat
ed f
orce
due
to m
isalig
n-m
ent,
and
bend
ing
stres
ses
beca
me
negl
igib
le. A
com
bi-
natio
n of
the
fille
t rad
ius
rede
sign
and
appl
icat
ion
of th
e ge
ar c
oupl
ing
addi
tiona
lly im
prov
ed fa
tigue
life
.
Bas
ed o
n th
is a
naly
sis,
the
actu
al s
ervi
ce li
fe o
f a s
haft
can
be im
prov
ed fr
om fi
nite
(3.5
·105 c
ycle
s) to
infin
ite
lifet
ime.
3.3.
3. C
orre
ctio
n
New
sha
fts w
ere
mad
e w
ith th
e ra
dius
siz
e du
e to
cha
nge
in th
e sha
ft di
amet
er 4
mm
and
the r
adiu
s siz
e in
the k
eyw
ay
corn
er 0
.6 m
m, m
inim
izin
g str
ess
conc
entra
tion
in b
oth
criti
cal a
reas
and
pre
vent
ing
recu
rrenc
e of
the
failu
re.
Split
muf
f co
uplin
gs w
ere
repl
aced
by
gear
cou
plin
gs
to r
educ
e th
e in
fluen
ce o
f pa
ralle
l m
isalig
nmen
t be
-tw
een
the s
haft
axis
and
the c
oupl
ing
axis
on lo
cal s
tress
es.
4. C
oncl
usio
n
The
failu
re a
naly
sis o
f tw
o ov
erhe
ad c
rane
shaf
ts sh
owed
th
at th
e ov
erhe
ad c
rane
driv
e sh
aft a
nd th
e ge
arbo
x sh
aft
fract
ured
as a
resu
lt of
rota
tiona
l-ben
ding
fatig
ue. I
n bo
th
case
s th
e fra
ctur
e oc
curre
d on
the
plac
es w
ith h
igh
stres
s co
ncen
tratio
n. T
he f
ract
ure
of th
e ov
erhe
ad c
rane
driv
e sh
aft o
rigin
ated
in th
e sm
all r
adiu
s fill
et b
etw
een
two
dif-
fere
nt d
iam
eter
s of t
he sh
aft.
The
fract
ure
of th
e ov
erhe
ad
cran
e gea
rbox
shaf
t was
initi
ated
in th
e int
erse
ctio
n of
two
stres
s rai
sers
on
the s
harp
corn
er in
the k
eyw
ay an
d on
the
radi
us o
f the
fille
t due
to ch
ange
in th
e sha
ft di
amet
er. T
he
failu
re a
naly
sis r
evea
led
that
the
desig
n lo
ad s
houl
d no
t ha
ve le
d to
shaf
t fra
ctur
e an
d th
at th
ere
also
exi
sted
addi
-tio
nal l
oad
unfo
rese
en b
y th
e de
sign.
The
pos
t-fai
lure
ver
-ifi
catio
n in
bot
h ca
ses
reve
aled
par
alle
l m
isalig
nmen
t be
twee
n tw
o sh
aft a
xes.
Corre
ctiv
e ac
tions
wer
e co
nsid
-er
ed i
n tw
o w
ays:
to i
mpr
ove
serv
ice
life
by a
sm
all
chan
ge in
the
desig
n an
d to
rem
ove
the
unfo
rese
en a
ddi-
tiona
l loa
d du
e to
misa
lignm
ent b
etw
een
two
shaf
t axe
s.
In th
e cas
e of t
he o
verh
ead
cran
e driv
e sha
ft, in
crea
sing
the
size o
f the
fille
t rad
ius f
rom
1.5
mm
to 5
mm
dec
reas
ed th
e m
axim
um lo
cal s
tress
bel
ow th
e en
dura
nce
limit,
resu
lting
in
sig
nific
ant i
ncre
asin
g of
the
fatig
ue li
fe. I
n th
e ca
se o
f th
e ove
rhea
d cr
ane g
earb
ox sh
aft,
incr
easin
g th
e rad
ius s
ize
due
to c
hang
e in
the
shaf
t dia
met
er fr
om 2
.5 m
m to
4 m
m
and
the
incr
easin
g of
the
radi
us s
ize
in th
e ke
yway
cor
ner
from
0.2
to 0
.6 m
m ex
tend
s the
fatig
ue li
fe m
ore t
han
twic
e.
The
gear
cou
plin
g, c
ompa
red
to th
e ro
ller c
hain
cou
plin
g an
d es
peci
ally
to sp
lit m
uff c
oupl
ing,
allo
ws m
ore
angu
lar
and
para
llel
misa
lignm
ent,
prol
ongi
ng s
igni
fican
tly s
haft
serv
ice
life.
Base
d on
this
anal
ysis,
the
actu
al s
ervi
ce li
fe
of th
e sha
ft ca
n be
impr
oved
from
fini
te to
infin
ite li
fetim
e.
Ref
eren
ces
[1]
Deu
tsch
es I
nstit
ut f
ür N
orm
ung.
DIN
172
00,
1987
(D
IN,
Ber
lin)
[2]
Cra
ne d
esig
n an
d m
anua
l boo
k of
bill
et o
verh
ead
cran
e in
“S
teel
wor
ks S
plit”
[3]
D.I.
D.,
“Pow
er t
rans
mis
sion
& c
onve
yor
chai
n”,
cata
log,
D
aido
Kog
yo c
o, K
umas
aka-
Cho
, Kag
a-C
ity, I
shik
awa
Pref
, 92
2-86
86, J
apan
, 200
7.[4
] W
.D. P
ilkey
, D.F
. Pilk
ey, “
Stre
ss c
once
ntra
tion
fact
ors”
, 3rd
ed.,
Hob
oken
, Joh
n W
iley
& S
ons,
New
Yor
k, 2
008.
[5]
E. H
eiba
ch, “
Bet
riebf
estig
keit“
, VD
I Ver
lag
Gm
bh, D
üsel
-do
rf, 1
989.
[6]
V. G
rubi
šić,
G.
Jaco
by,
“Fra
ctur
e an
alys
is,
valid
atio
n an
d te
chno
logi
es to
incr
ease
the
stre
ngth
of m
ater
ials
”, S
emin
ar,
Fire
nze,
Mar
ch 1
995.
[7]
SEIS
A, “
Gea
r cou
plin
g”, c
atal
og, S
eisa
Gea
r Ltd
., K
aizu
ka,
Osa
ka, J
apan
, 201
1.[8
] C
rane
des
ign
and
man
ual b
ook
of la
dle
over
head
cra
ne in
“S
teel
wor
ks S
plit”
[9]
Deu
tsch
es I
nstit
ut f
ür N
orm
ung.
DIN
171
00,
1980
(D
IN,
Ber
lin)
[10]
Deu
tsch
es I
nstit
ut f
ür N
orm
ung.
DIN
688
5-1,
Paß
fede
rn
nute
n, 1
968
(DIN
, Ber
lin)
[11]
Ž. D
omaz
et, “
Fatig
ue s
tress
con
cent
ratio
n fa
ctor
for
sha
ft w
ith d
iffer
ent k
eyw
ays
in b
endi
ng ”
, Ost
erre
ichi
sche
Ing
e-ni
eur u
nd A
rchi
tekt
en Z
eits
chrif
t, 14
2. J
g., H
eft 6
/199
7
Fig.
21.
Influ
ence
of c
orre
ctiv
e ac
tions
on
the
fatig
ue li
fe
top related