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1. STRUCURAL SCHEME, TORQUES AND ROTATION FOR
EACH SHAFT
1.1 Structural scheme
Figure 1
M - the electric engine
P - the power of the electric motor n - the rotation spead of the motor shaft
Mtn - the nominal torque at the motor shaft
Li - the ratial af the chain
I - the imput shaft
I T
- the torque of the imput shaft
I n - the rotation spead of the imput shaft
II - the output shaft
II
T
- the torque of the output shaft II n - the rotation spead of the output shaft
1 - the pinion
2 – the driver wheel
!"!#!$ – the %earings
r i - the spead redurer ratio
&.M. - the wor'ing machine
1
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1.2 (orque and rotations for each shaft
)ngine
Nmmn
P M
rot n
t *!+,-,1,*
/100!,100!,
min,*
**=⋅⋅=⋅=
=
Input shaft I3
Nmmi M M
rot i
nn
l ct tI
l c
I
,,2!/--/,2!1*!+,-,1
min42!1
,*
=⋅=⋅=
===
5utput shaft II3
Nmmi M M
rot i
nn
r tI tII
r
I II
/-!1*,01200!+,,2!/--/,
min+0!22000!+
4
=⋅=⋅=
===
2
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2. PROJECT PARAMETERS
INPUT DATA
2.1 Pinion speed n1! rotmin
n1 6 4 rotmin2.2 (he torsion torque at the pinion of the gearing (1! 7mm
(1 6 //,!,,2 7mm
2.+ 8earing ratio udat
udat 6 +!00
2./ Minimum functioning time of the gearing 9h! hours
9h 6 40 hours
2.0 Functioning conditions of the gearing
$river machine: electrical motor
$riven machine: fans
(;pe of load: uniform
2.* (he loading c;cles for the teeth
contact load : pulsator; c;cle
%ending load : pulsator; c;cle
2. 7um%er of load c;cles of the tooth flan'! at a full rotation χ1 for the pinion! χ2
for the driven wheel
χ1!2 6 1
2.4 (he reference rac' profile
For inclined teeth
αn 6 2< h=an 6 1!< c=
u 6 .20< ρ=fn 6 .+4
+
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3. CHOOSING THE MATERIALS, HEAT TREATMENTS AND THE
LIMIT STRESSES
+.1 #hoosing materials and treatments
&e choose /#r1 from S(S ,1
>ardness - e?ternal 0 >@#
- internal 2* >"
σr 6 , MPa
σ2 6 * Mpa
+.2 9imit stresses! σ>lim1!2! at contact and σFlim1!2 at %ending! MPa
σ>lim1!2 6 MPa
σFlim1!2 6 +2 MPa
/
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4. PRE-DIMENSIONING CALCULUS
/.1 7um%er of teeth A1! of the pinion! respectivel; A2 of the driven wheel.
12
-0
2/!+212cos100!+
2-0cos1
2ma?1
=
=
=°+
⋅=+
=
β
β
n
w
dat n
w
m
a
uma z
&e choose: +1 = z
0!1*00!++12 =⋅=⋅= dat u z z &e choose 1-2 = z
/.2 @eal gearing ratio u
+.24.
1
0*!++
1-
1
2
≤
∆≤−
===
uu
u
z
z u
dat
/.+ (he contact calculus factors B21!*C
/.+.1 (he elasticit; factor of the wheels material A)! MPa
MPa Z
MPa E E
E E
z
E
E
4!14,
1*!2
+!
11
1
021
21
2
2
2
1
2
1
=
⋅==
==
−+
−=
ν ν
ν ν π
/.+.2 (he contact area factor A>
/*.212cos/,!2cos/,!2 === β H z
/.+.+ (he covering factor Aε
0
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/.1
4/./.1
11
=
===
α
α
ε
ε ε
Z
/.+./ Inclining factor of the teeth Aβ
1!112cos
1
cos
1===
β β Z
/./ (he factor for the %ending calculus
/./.1 7um%er of teeth for the equivalent wheels
++2!11/12cos
1-
cos
00!+212cos
+
cos
++
22
++
11
===
===
β
β z
z
z z
n
n
/./.2 (he displacement coefficient of the profile in the normal plane ?n1!2
2!1 =n x
/./.+ Shape factor of the teeth DFa 1!2
14!23<++2!11/3!
0!23<00!+23!
222
111
===
===
Fann Fa Fa
Fann Fa Fa
Y x zY Y
Y x zY Y
/././ #orrection factor of stress DSa 1!2
--!13<++2!11/3!
*+!13<00!+23!
222
111
===
===
SannSaSa
SannSaSa
Y x zY Y
Y x zY Y
/./.0 #overing factor Dε
/.1
-*.12cos/.1
-0.20.cos
-0.20. 22
=
=+=+≈
α
α
ε
ε
β ε
Y
/./.* Inclined factor for the teeth Dβ
,.12
121
121 =
°
°−=
°
°−= β
β Y
/.0 9oad correction factor
/.0.1 (he functioning regime factor ' a
+0!1= Ak
/.0.2 $;namic factor ' v
1!1=vk
/.0.+ $istri%ution uneven3 factor for load on the width of the teeth ' >β for
contact and ' Fβ for %ending
*
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0!1
/0!1
=
=
β
β
F
H
k
k
/.0./ (he uneven distri%ution factor of the frontal plane ' >α at contact and
' Fα for %ending
/.1/*.112cos
/.1
cos 22 >====
β ε α
α α F H k k
/.* (he allowa%le resistances σ>P1!2 at contact and σFP1!2 for %ending BMPaC
-
222
4
111
1/,!11140+0!220**
14!/1404**
,2!
⋅=⋅⋅⋅==
⋅=⋅⋅⋅==
=
χ
χ
H L
H L
RV L
Ln N
Ln N
Z Z Z
MPaY Y Y S
Y Y
MPaY Y Y S
Y Y
MPa Z Z Z Z Z S
z
MPa Z Z Z Z Z S
z
S
z
z
z
z
x R
F
N ST F
FP
x R
F
N ST F FP
HP
! RV L
H
N H
HP
HP HP HP
! RV L
H
N H
HP
H
N
N
x
w
++!40+0!1
11122+2
**!/2*0!1
11112+2
+1!*13+0!*0,<+1!*1min
+0!*0,11,2.2.1
21!1--
3!min
+1!*111,2.2.1
12!1--
+!1
21!1
12!1
1
.1
22
min
22lim
2
11
min
11lim1
min
2lim
2
21
min
1lim
1
min
2
1
=⋅⋅⋅⋅⋅
==
=⋅⋅⋅⋅⋅==
==
=⋅⋅⋅⋅
==
=
=⋅⋅⋅⋅
==
=
=
=
==
δ
δ
σ σ
σ
σ
σ
σ σ
σ σ σ
σ
σ
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/. (he distance %etween the a?is at pre-dimensioning
/..1 &ide coefficient ψ a! ψ d
+!=aψ
ψ d 6 *4/!+!2
10*!+
2
1=
+=
+a
uψ
/..2 $istance %etween the a?is from the strength condition at contact aw>!mm
Z Z Z Z u
k k k k T ua H E
HP a
H H V A
wH
+!1+,31!14/./*.24.14,3+1!*10*!++!2
/*!1/0!11!1+0!1/*310*!+
32
31
+2
2
+ 2
2
1
=⋅⋅⋅⋅⋅⋅
⋅⋅⋅⋅+=
=Ψ
+= β ε
α β
σ
/..+ $istance %etween a?is from the strength condition at %ending a wF! mm
( )
/0.3!ma?
02!/-
/0!,!-*!/*!10!11!1+0!112cos+!2
10*!++/*
cos2
31
2
22
1
11
+
+
2
11
=
⋅⋅
=
⋅
=
=⋅⋅⋅⋅⋅⋅°⋅⋅
+⋅=
=+
=
FP
Sa Fa
FP
Sa Fa
FP
Sa Fa
FP
Sa Fa F F va
a
wF
Y Y Y Y Y Y mm
Y Y Y Y k k k k
u z T a
σ σ σ
σ β ψ β ε α β
/../ dopting the distance %etween the a?is at predimensioning aw! mm
aw 6 ma? aw>!awF3 6 ma? 1+,!+4</!023 6 1+,!+4mm <
&e adopt from S(S *00 the following aw 6 1/ mm.
/..0 (he preliminar; lengths of the wheels mma" ! a -,!/1+4!1+,+.2 =⋅==ψ
mm""" -,!/+2-,!/121 =+=∆+=
2<+...1 =∆=∆ ""
KINEMATIC SCHEME OF THE SPEAD REDUCER
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5. GEARING FORCES CALCULUS
0.1 Forces calculus
0.1.1 (angential force Ft! 7<
Figure. 0.1
N F F
N d
T F
t t
w
t
1,!10/*
1,!10/*-*/-1!*1
,,2!/--/,22
21
1
11
==
=⋅
==
0.1.2 @adial force Fr ! 7<
,
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N F F
N t# t# F
F
r r
wnt
r
1+!*-
1+!*-1+!2112cos
1,!10/*
cos
12
11
==
=⋅=⋅= α β
0.1.+ ?ial force Fa! 7<
Figure. 0.2
N F F
N t# t# F F
aa
t a
*0!+24
*0+!+24121,!10/*
21
11
==
=°⋅=⋅= β
0.2 #hoosing the sense of rotation and appl;ing forces
Figure. 0.+
1
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6. CALCULUS OF THE SHAFTS
*.1 Pre-dimensioning calculus:
mm
T
d atI
I
I +1.20101/!+
,,2!/--/,1*1*++ =⋅
⋅
=⋅
⋅
= τ π
mmT
d atII
II
II 4/!2-/2/!+
/-!1*,0121*1*++ =
⋅
⋅=
⋅
⋅=
τ π
*.2 #hoose of %earing mounting for input and output shafts:
Figure. *.1
d%3I!II 6 dI!II – 2E43mm
11
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(a%le *.1
d
BmmC
$ " r sBminC
Masa
B'gC
Sim%ol Sarcina radiala
$inamica Statica
dI 2 / 1/ 1 !114 *2/ 12! 0!
dII 20 02 10 1 !1/2 *20 1/ *!,0
*.+ #hec' of the input shaft for composed stresses.
*.+.1 >oriAontal plane
Figure *.2
"
@ > @ ">
Fr1
Fa1
[H
12
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N R F R
N l l
d F l F
R
d F l F l l R
M
AH r $H
w
ar
AH
w
ar AH
$
+!2/*!+*-1+!*-
*!+*-*101
2
-*/-1!*1*0!+24011+!*-
32
2
3
1
21
1
121
1
12121
=−=−=
=+
⋅+⋅=
+
⋅+⋅=
=⋅−−+
=Σ
*.+.2 ertical plane
Figure *.+
N R F R
N l l
l F R
l F l l R
M
AV t $V
t
AV
t AV
$
1+!4/2*!-/1,!10/*
*!-/01*1
011,!10/*
3
1
21
21
2121
=−=−=
=+
⋅=
+⋅
=
=⋅−+
=Σ
*./ $etermining of the reactions in the 2 %earings
@
l1
"
@ "
Ft1
[!
1+
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Figure *./
Nmml R M
Nmml R M
AH iH
AV iV
**!22+,*1*!+*-
**!/2,/-*1*!-/
1ma?
1ma?
=⋅=⋅=
=⋅=⋅=
*.0 Stresses identification
*.0.1 (orsion
MPad
T
%
t +*!1
3+///!0*1/!+
,,2!/--/,1*1*++
1
1=
⋅
⋅=
⋅
⋅=π
τ
*.0.2 "ending
MPad
M M
%
iV iH
i 2,!13+///!0*1/!+
3**!/2,-3**!22+,+2+2+
22
+
1
22
=⋅
+⋅=
⋅
+⋅=
π σ
*.* )quivalent stress
( ) aiIII &' σ τ α σ σ ≤⋅+= 22 /
( ) aiIII &' σ σ ≤=⋅+= -0!1+*!12-!/3/2!1 22
MPaict /2!12,!11+!3 =+=+= σ σ σ
MPad
F
%
act 1+!
3+///!0*1/!+
*0+!+24//22
1
13 =
⋅
⋅=
⋅
⋅=π
σ
°== 2-.aiI
aiIII
σ
σ α MPaaiIII ,=σ MPaaiI ++=σ
l1
"
Mih
Miv
Mt
(
1/
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". DESIGN OF THE ASSEM#LE #ET$EEN THE ENHECE AND
THE OUTPUT SHAFT
F%&'() ".1
&e choose from S(S 1/-41: %64< h6
,1!11-20
,,2./--/,//=
⋅⋅
⋅=
⋅⋅=
a(
t
c)d
M l
σ
MPaa( 1...*0=σ B1+C(o fi? the wheel 2 on the intermediate shaft is chosen to parallel t;pe G4G20 S(S
1/ – 41.
l 6 lc H % 6 1!,1 H 4 614!,1 mm
l62 mm S(S 1/-41
(a%le .1d % h
I 1/ 0 0
II 2 * *
II 20 4
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*. CHECH OF THE #EARING MONTINGS FOR THE IMPUT SHAFT
F%&'() *.1
02.*+
*0!+24==
o
A
*
F 6J e6!//
G61D6
& R R
F
F
F
AV AH
A
R
A≤=
+
=
+
= 1-.*!-/*!+*-
*0!+24
2222
1
+0!1,++2==⇒≤ R
R
A F P & F F
A R
R
A F Y F P & F
F ⋅+⋅=⇒≥
+
+2!1/++40/4+0!1,++2 +
=
=⋅=≤=
+
* L P * r
+
n&c
rot mil L)n
L I /41
404*
1
***
=⋅⋅
=⋅⋅
=
1*
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+. COOSING AND JUSTIFING THE OILING SSTEM AND
SEALING SSTEM
Oiling the gearings:
(he gears from speed reducers are grease through splashing in the oil %ath.
For this aim in which a gear from the gearing mechanism is introduce in the oil %ath until a tooth is covered with oil! not more than 1 mm! and without passingsi? time the modulus.
In case of speed reducers with more steps when the wheels dont reach the
%ath3! the grease is made with a parasite gear! or with the help of some discs or
splashing spoons which are creating am oil fog.
(he grease through splashing is applied on gearing mechanisms that are
wor'ing periodicall;! with speeds up to 10ms. For greater peripheral speeds! thegrease is done with oil inKectors. (he oil pressure is a%out .1-.4at. For greasing!
mineral oils are use with the viscosit; of +-* degrees )0L#.
$% /0 ' ) )(%)( ))7 % )(, ) /8 ()'()87 ) (/'&8) () %&)(, 87 /() 9%/' /% () ')7.
5n speed reducers with more gears! the oil is choused with a viscosit;
corresponding to the steps that transmit the %iggest torque. For the oil %ath
volume are considered .20-.0l of oil over a horsepower. (he period of oil change
is a%out 1-0 hours of functioning for the case when the gearing
mechanism is sealed and the oil is filtrate ever; 20 hours3. For filtering can %e
used magnetic filters. &hen the speed reducer is new! the oil must %e changed
after 2-+hours.
Oiling the ball-bearings:
(he choose of lu%ricants for %all %earings and esta%lishing the grease
intervals! is done considering the dimension! num%er of revolutions! load and wor'
temperature of the %earing.
8enerall;! the liquid lu%ricants have more advantages then the consistent
ones: higher ph;sical-chemical sta%ilit;! can %e used at high speeds and
temperatures! and also at ver; low temperatures! easier evacuation of heat
produced in the %earing! smaller resistance sported %; the rolling %odies.
$isadvantages: difficult %earing sealing! loses through lea'ages in time! etc.
8rease lu%rication is more advantageous %ecause leads to: simpler %earings
construction! eas; to seal! with a lower cost! %etter protection of the %alls to
e?ternal impurities! lower lu%ricant looses.
8as'ets: due to high levels of revolutions trees cuffs sealing is
accomplished %; rotation.
1
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1:.GHOOSING THE MATERIALA AND MANUFACTURING
SSTEM
It is choosen 14Mn#r11 steel hardening and tempering to achieve the shaft
and gear wheel transmission %ecause this steel has good resistance to %ending and
also has a high resistance to fatigue.
Materials used for speed reducer construction.
Materials used for gears:
Steel
It is used great steel: steel with car%on./-.* # and steel with .+0-./0#
low allo;ed with Mn! #r! #r-Mo! #r-7i etc. Steel non allo;ed with #r! #r6Mo! #r- 7i! with c;aniding
#ast irons
#ast irons are used at gearing which has a eas; wor'ing! change wheels which
dosent functioning ever; time.&hen it is as'ing a silent condition ma; %e usednormal iron ash.
Nsed material for a?els e?ecution:
8enerall; the a?el which don t have a heat treatment are made %; normall; steel
car%on: 59 0! 59 *! Stas 0-4For a?el which a %ig lifting power we can use car%on steel of qualit;: 59# +0!59# /0! 59# *! according to S(S 44-**.
In case of a?el which have a strong load and are required small dimension are used
steel allo;ed with crom! #r-7i or #r-Mn.
Marerials used for producing the body.
(he %od; %ecause of the stiffness are made %; cast irons or %; casting steel. Most
of the %od; are made %; cast iron with average resistance Fc 2! Fc 20.
14
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11.TECHNICAL SECURIT RULES $ORK
@educer %; definition in a speed reduction mechanism while increasing torque
transmition. 9i'e an; reducer mechanism involves compliance with specific
emplo;ment securit; tehmicaOs grave. It is a%solutel; mandator;:
-9ocation reducer in the vertical position< - 9u%ricant oil changes to term limits<
- @eplace %earings after the num%er of operating hours provided<
- n immediate replacement of an; assem%l; or su%assem%l; as soon as it
has found its damage<
- Fi?ing a reducer on the pedestal %efore putting it into operation<
- )?panding the level of lu%ricant if ;ou have found a fall %elow its
minimum<
- Periodic verification of the status reducer<
In prohi%its:
- Introducing lu%ricating oil other than reducing the limit<
- Introducing the reducing of an; material that could damage the gears<
- #hanging the oil or lu%ricant of an; assem%l; or su%assem%l; sin reducer
component during its operation<
- #logging ventilation holes<
1,
Recommended