corse project guide

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National Aviation University

MACHINE ELEMENTS

COURSE PROJECT DESIGN

Manual

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Revie4e5 6y7 senior resear89er: ;ro<* L*S*Novo=ru5s>yi: ;ro<*

O*O*?oron>o: asso8iate5 ;ro<* !*O*Koltsov

T9e En=lis9 lan=ua=e a5viser7 L*!*?u5>o

A;;rove5 6y t9e Met9o5i8al an5 E5itorial ?oar5 o< t9e National

Aviation University ,/*

М 13 MACHINE ELEMENTS. COURSE PROJECT DESIGN:

@anual Aut9ors7 A*S*KryB9anovs>yi: *O*Kornien>o:

O*!*?as9ta* K*7 NAU: "#$%* $"+ ;*

T9e @anual in8lu5es re8o@@en5ations <or 8arryin= out t9e

8ourse ;roe8t on t9e su6e8t FMa89ine Ele@ents an5 ea@;les

o< analysis an5 5esi=n o< 5ou6le sta=e s;ee5 re5u8ers*

T9e @anual is inten5e5 <or stu5ents o< 5ire8tion )*#-#$#3FAir8ra<t Maintenan8e*

"



INTRODUCTION

T9e 8ourse ;roe8t on t9e su6e8t F Machines Elements” is one o<

t9e 6asi8 >in5s o< t9e stu5ents in5ivi5ual 4or>* T9e ;ur;ose o< t9e

8ourse ;roe8t is to en9an8e t9e >no4le5=e a8uire5 6y t9e stu5ent at

t9e le8tures: ;ra8ti8al 8lasses an5 la6oratory sessions as 4ell as to

5evelo; t9e s>ills o< @a>in= resear89 an5 5esi=n o< ;resent5ay s;ee5

re5u8ers*

T9e 8ourse ;roe8t is to in8lu5e t9e <ollo4in= ;arts7

$* Deter@ination o< s;ee5 re5u8er ele@ents =eo@etri8al

;ara@eters an5 8arryin= out t9eir stren=t9 analysis*

"* Desi=nin= a s;ee5 re5u8er*

3* Desi=nin= a @e89ani8al 5rive*All 8al8ulations are to 6e ;resente5 at t9e e;lanatory note t9at

s9oul5 6e 8arrie5 out a88or5in= to reuire@ents o< State Stan5ar5

'& 3##+.* 'QV WXYX &Z[* '\Z]^X_`1* `X

Wb` ]Z ` Xc`Z* X]ZX] ` d \b\^1f* T9e

e;lanatory note s9oul5 6e eit9er ty;e5 or 9an5 4ritten in 6lue or 6la8>

in> on one si5e o< siBe A% ;a;er* Every s9eet is to 6e ;a=inate5 an5 9ave

t9e <ollo4in= @ar=ins7 to; . @@: 6otto@ . @@: ri=9t . @@: an5

le<t "# @@*?esi5es 8al8ulations t9e e;lanatory note s9oul5 9ave t9e

8ontents ta6le: t9e assi=n@ent: t9e re<eren8e literature use5 <or @a>in=

t9e 8ourse ;roe8t: s;e8i<i8ations* Ea89 ne4 ;art s9oul5 6e 6e=un 4it9 a

ne4 ;a=e*

Ea89 ;art @ust 6e su65ivi5e5 into ite@s @ar>e5 4it9 nu@erals

se;arate5 6y a ;oint* T9e <irst nu@eral re;resents t9e nu@6er o< t9e

;art: t9e se8on5 one s9o4s t9e nu@6er o< t9e ite@*

All @a=nitu5es t9at are t9e ;art o< <or@ulas s9oul5 6e e;laine5*?esi5es: it is ne8essary to 5enote @easure@ent units o< ;ara@eters

6ein= 8al8ulate5*

T9e =ra;9i8al ;art 8onsists o< % 5ra4in=s7 t9e <irst 5ra4in= is a

s;ee5 re5u8er , t4o ;roe8tions/g t9e se8on5 5ra4in= is a @e89ani8al

5rive ,t4o ;roe8tions/g t9e t9ir5 5ra4in= is s9o; 5ra4in= o< a s;ee5

re5u8er s9a<tg t9e <ort9 5ra4in= is s9o; 5ra4in= o< a s;ee5 re5u8er =ear*

T9e <irst an5 t9e se8on5 5ra4in=s are @a5e on A$ 49at@an ;a;erg t9e

t9ir5 an5 t9e <ort9 5ra4in=s are @a5e on A3 49at@an ;a;er* T9e title

6lo8> s9oul5 6e 5ra4n in t9e 6otto@ ri=9t 9an5 8orner*

3



$* KINEMATIC AND hORCE ANALSIS Oh

A MECHANICAL DRI!E

Let us 5eter@ine t9e 6asi8 ;ara@eters o< t9e @e89ani8al 5rive,hi=* $*$/ i< ;ull o< t9e 6elt F t 3 >Ng 6elt s;ee5 V $*% @se8g 5ru@

5ia@eter D3.# @@*

%



.



hi=* $*$* Dia=ra@ o< sin=le sta=e s;ee5 re5u8er 4it9 89ain 5rive

$*$* Deter@ine t9e out;ut ;o4er o< t9e 5rive

P out = F t ⋅V 3j$*%%*" >k$*"* Deter@ine t9e total e<<i8ien8y o< t9e 5rive

In =eneral

ηη$⋅η"⋅*⋅ηn :

49ere η$:η":*ηn are e<<i8ien8ies o< all >ine@ati8 ;airs an5 lin>s 49ere

t9e in;ut ;o4er is lost*

hor our 8ase

η ηc ⋅ ηhsg ⋅ ηcd ⋅ηb3:

49ere ηc is t9e e<<i8ien8y o< t9e 8ou;lin=gηhsg is t9e e<<i8ien8y o< 9eli8al s;ur =earsg

ηcd is t9e e<<i8ien8y o< t9e 89ain 5riveg

ηb ta>es into a88ount losses in one ;air o< 6earin=s*

T9e @a=nitu5es o< all e<<i8ien8ies are =iven in ta6le $*$*

T9e <ollo4in= 8o@;onents are re8o@@en5e5 to use <or

@e89ani8al 5rives 6ein= analyBe57

6elt 5rive 4it9 <lat 6eltg

89ain 5rive 4it9 roller 89aing rollin= 6earin=sg

8ou;lin= 4it9 ru66er 6us9e5 stu5sg Table 1.1

The magnit!e" #$ e$$i%ien%ie" #$ the !&i'e"

Na@eE<<i8ien8y

Close5 5rive O;ene5 5rive

Gea&ing":

strai=9t s;ur =ears 9eli8al s;ur =ears 6evel =ears(#&m gea&ing:

one t9rea5 4or@ t4o t9rea5 4or@ <our t9rea5 4or@)e*t !&i'e":

<lat 6elt 5rive !6elt 5rive

Chain !&i'e":

#*+ #*#*- #*+#*) #*+

#*- #*-.#*-. #*+"#*+" #*"

#*% #*)#*% #*.#*" #*%

#*) #*+#*. #*-

)



roller 89ain toot9e5 89ainC#+*ing":

4it9 ru66er 6us9e5 stu5s

<lei6le 8ou;lin=ri=i5 8ou;lin=)ea&ing":

rollin= 6earin=s sli5in= 6earin=s

#*)

#*+. #*.$

#* #*.#*+ #*+.

#*% #*)#*) #*-

Let us assu@e t9at ηc #*): ηhsg #*-:

ηcd #*%: ηb #** T9en

η #*) ⋅ #*- ⋅ #*% ⋅ #*3 #*++$*

Pay attention t9at t9e @a=nitu5e o< t9e total e<<i8ien8y @ust 6eroun5e5 o<< to t9ousan5t9 or ten t9ousan5t9*

$*3* Deter@ine t9e in;ut ;o4er*In =eneral t9e e<<i8ien8y is 5eter@ine5 as ratio o< t9e out;ut

;o4er to t9e in;ut one

out

inp

P

P η =

T9at is 49y 4e 8an <in5 nee5e5 ;o4er o< t9e ele8tri8al @otor %*"

%*-)-#*++$

out inp

P P kW = = =

η *

$*%* Sele8t t9e ele8tri8al @otor*

hor =iven @e89ani8al 5rives 4e 4ill use asyn89ronous ele8tri8al

@otor* It is e;laine5 6y t9e <a8t t9at in 8o@;arison 4it9 t9e ot9er ty;es

o< @otors asyn89ronous ele8tri8al @otors are si@;ler in 5esi=n an5

@aintenan8e: @ore relia6le an5 less e;ensive* T9e @ost 4i5ely s;rea5

asyn89ronous @otors are series %A suirrel 8a=e in5u8tion @otors*Asyn89ronous @otors are 89osen 6y @eans o< ta6le $*"

5e;en5in= on t9e in;ut ;o4er P inp o< a @e89ani8al 5rive an5 t9e

syn89ronous rotational s;ee5 n s ,rotational s;ee5 o< a @a=neti8 <iel5

49i89 89ara8teriBes o;eration o< t9e @otor 4it9out loa5/* hor =iven

@e89ani8al 5rives asyn89ronous @otors are use5 eit9er syn89ronous

rotational s;ee5 n s $.## r;@ or n s $### r;@*

Table 1.2.

Pa&amete&" #$ a",n%h&#n#" m#t#&"Syn89ronous rotational s;ee5 n s: r;@

-



Rate5

;o4er

P : >k

$.## $### -.#

Ty;e

5esi=nation

! :m Ty;e

5esi=nation

! :m Ty;e

5esi=nation

! :m

#*.. -$A% -*3 -$?) $# +#?+ #*-. -$?% -*. +#A) +*% #LA+ +*%

$*$ +#A% .*% +#?) +*# #L?+ -*#

$*. +#?% .*+ #L) )*% $##L+ -*#

"*" #L% .*$ $##L) .*$ $$"MA+ )*#

3*# $##S% %*% $$"MA) %*- $$"M?+ .*+

%*# $##L% %*- $$"M?) .*$ $3"S+ %*$

.*. $$"M% 3*- $3"S) 3*3 $3"M+ %*$

-*. $3"S% 3*# $3"M) 3*" $)#S+ "*.

$$*# $3"M% "*+ $)#S) "*- $)#M+ "*.$. $)#S% "*3 $)#M) "*) $+#M+ "*.

$+*. $)#M% "*" $+#M) "*- "##M+ "*3

hor our @e89ani8al 5rive 4e sele8t %A$3"S) In5u8tion Motor

, P .*. >k: n s $.## r;@/*

$*.* Deter@ine t9e @otor rate5 rotational s;ee5 n

,$ / :$##

= − s

! n n

49ere ! is relative s;ee5 loss t9at is 5eter@ine5 a88or5in= to ta6le $*"*

In our 8ase ! 3*3 m* A<ter su6stitutin= 8orres;on5in= @a=nitu5es 4e

o6tain

3*3$### ,$ / )- r;@*

$## n = × − =

$*)* Deter@ine t9e out;ut rotational s;ee5

)# )# $*%-)*%3 r;@*

3*$% #*3.out

V n

D

× ×= = =

π× ×$*-* Deter@ine t9e total velo8ity ratio o< t9e @e89ani8al 5rive

)-$"*).

-)*%3

inp

out

nu =

n= =

*

$*+* Distri6ute t9e total velo8ity ratio 6et4een @e89ani8al 5rive

ste;s* T9e total velo8ity ratio 8an 6e <oun5 6y t9e <or@ula

u = ued ⋅ ucd :

+



49ere ued is t9e s;ee5 re5u8er velo8ity ratiog ucd is t9e 89ain 5rive

velo8ity ratio*

hirst: 5eter@ine t9e velo8ity ratio o< t9e s;ee5 re5u8er*

hor strai=9t s;ur =ears: 9eli8al s;ur =ears an5 6evel =ears s;ee5re5u8ers t9e velo8ity ratio s9oul5 6e 89osen <ro@ t9e <ollo4in= stan5ar5

series ued $*".g$*%g$*)g$*+g"g"*"%g"*.g"*+g3*$.g3*..g%g%*.g.g.*)*

hor 4or@ =ear s;ee5 re5u8ers ued is ta>en <ro@ t9e <ollo4in=

stan5ar5 series ued +g$#g$"*.g$)g"#g".g3$*.g%#g.#g)3g+#*

In our 8ase 4e 9ave 9eli8al s;ur =ears s;ee5 re5u8er* Let us ta>e

ued =uhsg %*

Deter@ine t9e velo8ity ratio o< t9e o;en 5rive* In our 8ase it is89ain 5rive

$"*).3*$)*

%cd

ed

uu

u= = =

O6taine5 value o< t9e velo8ity ratio o< t9e o;en 5rive s9oul5

satis<y to t9e <ollo4in= 8on5ition* hor 89ain 5rives ucd is to 6e ran=e5

<ro@ $*. to %: <or 6elt 5rives ubd is to 6e ran=e5 <ro@ " to %: <or strai=9t

s;ur =ears u ssg is to 6e ran=e5 <ro@ " to .* I< t9is 8on5ition is not

satis<ie5 4e ta>e t9e ot9er value o< ued <ro@ t9e stan5ar5 series*

$** Deter@ine t9e rotational s;ee5 o< all s9a<ts

n$ n )- r;@g

$"

)-"%$*-. r;@g

%hsg

nn

u= = =

"

3

"%$*-.

-)*. r;@*3*$)cd

n

n u= = =O6taine5 @a=nitu5e o< n3 @ust 6e eual to nout 8al8ulate5 a88or5in=

to ;* $*)* Error @ust 6e not @ore t9an $m* In our 8ase #*#m*

$*$#* Deter@ine t9e an=ular velo8ity o< all @e89ani8al 5rive s9a<ts

$$$

3*$% )-$#$*"$se8 g

3# 3#

n −π ×ω = = =

J$$"

$#$*"$ ".*3 se8 g

%hsg u

ωω = = =



J$"3

".*3 +*##- se8 *3*$)cd u

ωω = = =

1.11. Deter@ine t9e ;o4er at @e89ani8al 5rive s9a<ts*

Cal8ulation is 8arrie5 out <or P inp: 5eter@ine5 in ;*$*3* P $ = P inp ⋅ηc⋅ηb %*-)-⋅#*)⋅#* %*- >kg

P " = P $⋅ηhsg ⋅η b %*-⋅#*-⋅#* %*.$% >kg

P 3 = P "⋅ηcd ⋅η b %*.$%⋅#*%⋅#* %*"#$ >kg

O6taine5 @a=nitu5e o< P 3 @ust 6e eual to P out 8al8ulate5

a88or5in= to t9e ;*$*$* Error s9oul5 not 6e =reater t9an $m* In our 8ase

#*#"m*

$*$"* Deter@ine t9e torues at all s9a<ts*3

$$

$

%*- $#%)*%3+ N @g

$#$*"$

P T

×= = = ×

ω3

""

"

%*.$% $#$-+*%$ N @g

".*3

P T

×= = = ×

ω3

33

3

%*"#$ $#."%*))) N @*

+*##-

P T

×= = = ×

ω

C9e8>in=*

T9e out;ut torue T out 8an also 6e <oun5 as3

3 $# #*3..". N @*

" "out t

DT F

× ×= = = ×

Deter@ine t9e error* It s9oul5 6e less t9an $m*

."%*))) .".$##m #*#)3 m*

.".

−ε = × =

$#



-. ANALSIS O/ ALLO(A)LE STRESSES

Let us analyse t9e s;ee5 re5u8er o< t9e @e89ani8al 5rive 49en7 n p =

)- r;@g n g "%$*-. r;@*

ke 4ill 6e=in <ro@ t9e sele8tion o< t9e @aterial o< =ears an55eter@ination o< t9eir allo4a6le 8onta8t an5 6en5in= stresses*

"*$* Sele8t t9e @aterial o< toot9e5 49eels*

T9e @ain @aterial o< toot9e5 49eels is 8ar6on or alloy steels*

De;en5in= on @aterials 9ar5ness toot9e5 49eels are su65ivi5e5 into

t4o =rou;s7

toot9e5 49eels 4it9 sur<a8e 9ar5nessH 3.# ?HN≤

g

toot9e5 49eels 4it9 sur<a8e 9ar5nessH 3.#?HN>

*

hor =eneral ;ur;ose s;ee5 re5u8ers t9e <ollo4in= alternatives are ;ossi6le7

$* A ;inion an5 a =ear are ;ro5u8e5 <ro@ i5enti8al 8ar6on or alloy steel:

su89 as Steel %. ,#*%.C/: Steel %#p ,#*%#CCr/: Steel %#pH ,#*%#CCr

Ni/* Heat treat@ent o< 6ot9 t9e =ear an5 t9e ;inion is @arte@;erin=* T9e

;inion 9ar5ness is ran=e5 <ro@ ") to 3#" ?HN an5 t9e =ear 9ar5ness is

ran=e5 <ro@ "3. to ")" ?HN*

"* A ;inion an5 a =ear are ;ro5u8e5 <ro@ i5enti8al alloy steel: su89 as

Steel %#p ,#*%#CCr/: Steel %#pH ,#*%#CCrNi/: Steel 3.pM ,#*3.CCrMo/* Heat treat@ent o< t9e =ear is @arte@;erin= to 9ar5ness ran=e5

<ro@ ") to 3#" ?HN* Heat treat@ent o< t9e ;inion is @arte@;erin= an5

sur<a8e ,in5u8tion/ 9ar5enin= to 9ar5ness ran=e5 <ro@ %. to .# HRC*

Toot9e5 49eels o< t9e strai=9t s;ur =ears an5 9eli8al s;ur =ears are

re8o@@en5e5 to ;ro5u8e a88or5in= to t9e $st alternative* I< 4e 5eal

4it9 6evel =ears 4e 8an use eit9er t9e $st or t9e "n5 alternative*

"*"* Deter@ine t9e @ean @a=nitu5e o< t9e 9ar5ness o< t9e =ear an5

t9e ;inion7

<or t9e ;inion

; ;@a@in ;

@H H

gH"

+=

<or t9e =ear

= =@a@in=

@H H

*H"

+=

In our 8ase a ;inion an5 a =ear are ;ro5u8e5 <ro@ i5enti8al alloy

steel o< =ra5e Steel %#pH an5 4e use t9e $st alternative ,9eat treat@ent

o< t9e =ear is @arte@;erin= to 9ar5ness ran=e5 <ro@ "3. to ")" ?HNg

9eat treat@ent o< t9e ;inion is @arte@;erin= to 9ar5ness ran=e5 <ro@

$$



") to 3#" ?HN/7

;@

") 3#""+.:.H

"

+= =?HNg

=@

"3. ")""%+*.H

"

+= =

?HN*

"*3* Deter@ine t9e allo4a6le 8onta8t stress <or t9e ;inion an5 <or t9e=ear*

"*3*$*Deter@ine t9e li@it o< 8onta8t en5uran8e <or t9e ;inion ;

H li@σ

an5 <or t9e =ear=

H li@σa88or5in= to t9e ta6le "*"*

li@ " -# " "+.*. -# )%$= × + = × + = p p

" m " MPaσ

li@ " -# " "%+*. -# .)-= × + = × + = g g

" m " MPaσ

"*3*"*Deter@ine t9e 6ase nu@6er o< stress 8y8les <or t9e ;inion ;

H# N

an5 <or t9e =ear =

H# N* hor t9is ;ur;ose 4e use ta6le "*$*

Table 2.1

)a"e nm0e& #$ "t&e"" %,%*e"

?HN@ u; to "## ".# 3## 3.#%#

#%.# .##

..

#

)#

#

HRC@ ". 3" 3+ %3 %- ." .) )#

NH#q$#) $# $)*. ". 3)*% .# )+ +- $$%$%

3

; )

H# N ""*. $#= × stress 8y8lesg= )

H# N $)*3 $#= × stress 8y8les.

"*3*3* Deter@ine t9e servi8e li<e in 9ours <or t9e =earin=7

t L q 3). q K a q "% q K 5:

49ere # is t9e servi8e li<e in yearsg $ a is t9e annual utiliBation <a8tor

49i89 is use5 to ta>e into a88ount use o< t9e =earin= 5urin= a yearg $ d

is t9e 5aily utiliBation <a8tor 49i89 is use5 to ta>e into a88ount use o<

t9e =earin= <or "% 9ours* T9ese ;ara@eters s9oul5 6e =iven in t9e

s;e8i<i8ation <or t9e ter@ ;a;er*

In our 8ase t9e servi8e li<e o< t9e =earin= is - years: K a #*.: K 5 #*3- 3). #*. "% #*3 $+ 9ours= × × × × =t *

"*3*%* Deter@ine t9e 5esi=n nu@6er o< stress 8y8les <or t9e ;inion

$"



an5 t9e =ear* ; ;

Hi N )# n 8 tg= × × ×

= =

Hi N )# n 8 t= × ×

49ere n p an5 n g are 8orres;on5in=ly rotational s;ee5s o< t9e ;inion an5

t9e =earg c is t9e nu@6er o< =ears @es9in= 4it9 t9e =ear 6ein= analyse5*

In our 8ase 8 $: n ; )- r;@g n= "%$*-. r;@* ; )

Hi N )# )- $ $+ .33:))+ $# g= × × × = ×

= )

Hi N )# "%$:-. $ $+ $33:%$- $#= × × × = ×

*

Table 2.2C#nta%t an! 0en!ing *imit" #$ en!&an%e

Heattreat@ent

Toot9 9ar5ness

Gear @aterial :MPa " limσ :MPab limσ8ase

8ore an5

root

Nor@aliBin=:

@arte@;erin=?rinell $+# to 3.#

Car6on an5 alloy

steels: su89 as %.,#*%.C/: %#p ,#*%#C

Cr/: %#pH ,#*%#C

CrNi/: .#pH,#*.#CCrNi/: an5

3.pM ,#*3.CCr

Mo/

" -#m

" + $*+m

"

hull

9ar5enin=Ro8>4ell C: %# to ..

Car6on an5 alloysteels: su89 as %.

,#*%.C/: %#p ,#*%#C

Cr/: %#pH ,#*%#CCrNi/: an5 3.pM

,#*3.CCrMo/

$+ $.#m

" + .##

Sur<a8e

9ar5enin=

Ro8>4ell C:

%# to .+

Ro8>4ell C:

". to 3.

Alloy steels: su89 as%#p ,#*%#CCr/:

%#pH ,#*%#CCrNi/:

.#pH ,#*.#CCrNi/:

an5 3.pM ,#*3.CCrMo/

$- "##m " + ).#

Case9ar5enin=

Ro8>4ell C:.% to )%

Ro8>4ell C:3# to %.

Alloy steels: su89 as"#pH"M ,#*"#CCr

"NiMo/

"3 m " .#

$3



Nitri5in=Ro8>4ell C:

.# to )#

Ro8>4ell C:

"% to %#

Alloy steels: su89 as

%#pH"MA ,#*%#CCr"NiMo: uality/

$#.#

3## $*" m " +,o< toot9

8ore/

"*3*.* Deter@ine t9e 5ura6ility <a8tor <or t9e ;inion an5 <or t9e =ear*

i< NHi NHO t9en K HL$:

i< NHi NHO t9en

H#)

HL

Hi

NK

N=

*

In our 8ase ; )H# N ""*. $#= × :

; )Hi

N .33:))+ $#= × % ; ;Hi H#

N N> :

8onseuently ;

HLK $g== )

H# N $)*3 $#= ×

: )

Hi N $33:%$- $#= ×

% ; ;

Hi H# N N> :

8onseuently=

HLK $*=

"*3*)* Deter@ine t9e sa<ety <a8tor ! " <or t9e ;inion an5 <or t9e =ear*

<or 9o@o=eneous stru8ture o< t9e @aterial

,9eat treat@ent is nor@aliBin=: @arte@;erin=

an5 <ull 9ar5enin=/ SH $*$g

<or 9etero=eneous stru8ture o< t9e @aterial

,9eat treat@ent is sur<a8e 9ar5enin=:

8ase 9ar5enin=: nitri5in=/ SH $*"*

"*3*-* Deter@ine t9e 8onta8t allo4a6le stresses <or t9e =ear an5 <or

t9e ;inion ;

; Hli@ HL

H ;

H

K

:S

σ × σ =

== H li@ HL

H =

H

K

S

σ × σ = *

In our 8ase7 $*$g= = p g

" " ! !

;

H

)%$ $.+"*-3MPag

$*$

× σ = =

=

H

.)- $.$.*%..MPa

$*$

× σ = = *

I< H ;H= ≤ -#?HN: 4e assu@e as t9e 5esi=n allo4a6le 8onta8t

stress t9e less @a=nitu5e o< a6ove 8al8ulate5 stresses: 49ere H ; an5 H=

are 8orres;on5in=ly 9ar5ness o< t9e ;inion an5 =ear @aterials*

$%



Ot9er4ise: t9e 5esi=n allo4a6le 8onta8t stress is 5eter@ine5 6y t9e

<ollo4in= <or@ula

[ ] ( ) ; = =

H H H H#*%. $*"3 σ = × σ + σ ≤ × σ *In our 8ase H ;H= -#?HN* T9at is 49y <or <urt9er 8al8ulations 4e

ta>e as t9e 5esi=n allo4a6le 8onta8t stress[ ]H .$.*%..MPaσ =

*

"*%* Deter@ine t9e allo4a6le 6en5in= stresses o< t9e ;inion an5 t9e =ear*

"*%*$ * Deter@ine t9e li@its o< t9e 6en5in= en5uran8e <or t9e ;inion ;

6 li@σ an5

<or t9e =ear =

6 li@σ

* hor t9is ;ur;ose 4e use ta6le "*$* ;

6 li@

$*+ "+.*. .$3*MPaσ = × =*

=

6 li@

$*+ "%+*. %%-:3MPaσ = × =

"*%*"* Deter@ine t9e 6ase nu@6er o< stress 8y8les 6# N *

hor steels 6# N %j$#)*

"*%*3* Deter@ine t9e 5esi=n nu@6er o< stress 8y8les <or t9e ;inion

an5 t9e =ear* ;

6i ; N )# n 8 tg= × × ×=

6i = N )# n 8 t= × ×

g ; ; )

6i Hi N N .33:))+ $# g= = ×= = )

6i Hi N N $33:%$- $#= = ×

*

"*%*%* Deter@ine t9e 5ura6ility <a8tor <or t9e ;inion an5 <or t9e =ear*

i< N 6i N 6# t9en K 6L$:

i< N 6i N 6# t9en

6#@

6L

6E

NK

N=

:

49ere @3 <or toot9e5 49eels 4it9 9ar5ness H 3.# ?HN an5 @ i< H 3.# ?HN*

In our 8ase7 ; ;

6i 6# N N>

: 8onseuently ;

6LK $g== =

6i 6# N N> : 8onseuently

=

6LK $*=

"*%*.* Deter@ine t9e sa<ety <a8tor S 6 <or t9e ;inion an5 <or t9e =ear*

<or 49eels @a5e o< <or=e5 6lan>s ,our 8ase/ S 6 $*-.g

<or 49eels @a5e o< 8ast 6lan>s S 6 "*3*

"*%*)* Deter@ine t9e 6en5in= allo4a6le stresses <or t9e =ear an5 <or

$.



t9e ;inion ;

; 6li@ 6L 6 ;

6

K

S

σ × σ = :

== 6li@ 6L 6 =

6

K

S

σ × σ = *

In our 8ase7$*-.g p g

b b! ! = =

;

6

.$3: $"3*))MPag

$*-.

× σ = = =

6

%%-:3 $"..*)MPa

$*-.

× σ = =

hor <urt9er 8al8ulations: 4e assu@e as t9e 5esi=n allo4a6le 6en5in=

stress t9e less @a=nitu5e o< a6ove 8al8ulate5 stresses[ ] 6 "..*)MPaσ =

*

$)



3. ANALSIS O/ THE STRAIGHT SPUR GEARS /OR

STRENGTH

Let us 8arry out t9e analysis o< t9e strai=9t s;ur =ears <or stren=t9

i< torue at t9e ;inion s9a<t T p -% N⋅@g torue at t9e =ear s9a<t T g 3-#

N⋅@g velo8ity ratio o< t9e =earin= u.g allo4a6le 8onta8t stress

w " x.$.:%.. MPag allo4a6le 6en5in= stress wbx"..:) MPag 9ar5ness

o< t9e =ear @aterial " g "+. ?HN: an=ular velo8ity o< t9e =ear s9a<t

g %# ra5se8*

3*$* Deter@ine t9e 8entre 5istan8e o< t9e strai=9t s;ur =ears

( ) 3" "

#*+. $

x

g " t

&

" ba

T $ E a u

u

β× ×= × ± ×

× ×σ ψ :49ere u;;er si=n ,Fz/ is ri=9t <or =ears 4it9 eternal toot9in= an55o4n si=n ,F/ is ri=9t <or =ears 4it9 internal toot9in=g u is t9e velo8ity

ratio o< t9e =earin=g T g is t9e torue at t9e =ear s9a<t in N⋅@@g w " x is

t9e allo4a6le 8onta8t stress in MPag E t is t9e trans<or@e5 @o5ulus o< elasti8ity in MPag $ " { is t9e loa5 8on8entration <a8torg |ba b g 'a& is t9e=ear <a8e 4i5t9 <a8tor*

Trans<or@e5 @o5ulus o< elasti8ity E t is 5eter@ine5 as

"

p g

t p g E E E = E ( E × ×

:

49ere E p an5 E g are 8orres;on5in=ly @o5uli o< elasti8ity o< ;inion an5

=ear @aterials* Sin8e t9e ;inion an5 t9e =ear are @a5e o< steel 4e 8an

@a>e t9e 8on8lusion t9at E t = E p = E g = "*$⋅$#. MPa*

Loa5 8on8entration <a8tor $ " { is 5eter@ine5 6y @eans o< ta6le 3*"

5e;en5in= u;on 5is;osition o< toot9e5 49eels 4it9 res;e8t to 6earin=s

an5 <a8tor |bd b g d p* Sin8e b g an5 d p 4ere not 5eter@ine5 4e <in5 t9is

<a8tor 6y t9e <ollo4in= <or@ula

( ) ( )#*.

$ #*. $ g g

bd ba p&

b bu u

d a

×ψ = = × ± = × ψ × ±

:

49ere t9e =ear <a8e 4i5t9 <a8tor |ba is 5eter@ine5 <ro@ ta6le 3*$

5e;en5in= u;on t9e 5is;osition o< t9e =ear relative to 6earin=s an5

ta>in= into a88ount t9at t9e value o< |ba s9oul5 8orres;on5 to stan5ar5*

T9e =reater |ba 8orres;on5s to t9e less overall 5i@ensions o< t9e =earin=*

In our 8ase t9e =ear is lo8ate5 sy@@etri8ally 4it9 res;e8t to

su;;orts* T9at is 49y |ba#:.: #*. #*. ,. $/ $*.ψ = × × + =bd an5 $ " {$*$$*

$-



( )3 .

3" "

3-# $# $*$$ "*$ $##*+. . $ $.$@@

.$.: %.. . #*.

× × × ×= × + × =

× ×&a

ke roun5 o<< o6taine5 @a=nitu5e o< a& to t9e nearest =reater si5e

a88or5in= to t9e series =iven in ta6le 3*3* ke assu@e a&$)# @@*

Table ).1Re%#mmen!e! 'a*e" #$ the gea& $a%e i!th $a%t#& 2ba

Gear arran=e@ent 4it9

res;e8t to 6earin=sToot9 9ar5ness |ba

Sy@@etri8al Any #*3$.g #*%g #*.

Nonsy@@etri8al ?rinell ?HN: u; to 3.#

Ro8>4ell C: %# u;4ar5s

#*3$.g #*%

#*".g #*3$.On s9a<t 8antilevers ?rinell ?HN: u; to 3.#

Ro8>4ell C: %# u;4ar5s

#*".

#*"

hor 9errin=6one =ears Any #*% g #*.g #*)3

hor internal =ears Any #*"

Table ).2A++&#imate 'a*e" #$ K H 4

Gear

arran=e@ent

4it9 res;e8t to 6earin=s

Toot9

sur<a8e

9ar5ness:?HN

=

65 ;

6

5ψ =

#*" #*% #*) #*+ $*" $*)

On 8antilevers:

6all 6earin=s

u; to 3.#

over 3.#

$*#+

$*""

$*$-

$*%%

$*"+

On 8antilevers:

roller 6earin=s

u; to 3.#

over 3.#

$*#)

$*$$

$*$"

$*".

$*$

$*%.

$*"-

Sy@@etri8alu; to 3.#

over 3.#

$*#$

$*#$

$*#"

$*#"

$*#3

$*#%

$*#%

$*#-

$*#-

$*$)

$*$$

$*")

Nonsy@@etri8a

l

u; to 3.#

over 3.#

$*#3

$*#)

$*#.

$*$"

$*#-

$*"#

$*$"

$*"

$*$

$*%+

$*"+

Table ).)

Stan!a&! 'a*e" #$ the %ent&e !i"tan%e aw

Series

$

)3 +# $## $". $)# "## ".# 3$. %## .##

Series

"

-$ # $$" $%# $+# ""% "+# 3.. %.# .)#

3*"* Deter@ine t9e no@inal ;it89 8ir8le 5ia@eter o< t9e =ear

$+



" " $)# .")):)-@@

$ . $

× × × ×= = =

± +& g a u

d u *

3*3* Deter@ine t9e <a8e 4i5t9 o< t9e =ear

b g |ba ⋅ a&#*.j$)#+# @@*3*%* Deter@ine t9e @o5ule a88or5in= to t9e stren=t9 8on5ition <or

6en5in=3" " )*+ 3-# $#

#*3@@")):)- +# "..:) x

× × × × ×≥ = =

× ×× × σ

g

m

g g

b

$ T m

d b:

49ere $ m is ta>en as )*+ <or strai=9t s;ur =ears*

O6taine5 @a=nitu5e o< t9e @o5ule s9oul5 6e roun5e5 o<< to t9e

=reater si5e a88or5in= to t9e stan5ar5 series =iven in ta6le 3*%* It isne8essary to note t9at <or =eneral;ur;ose s;ee5 re5u8ers t9e @ini@u@

value o< t9e @o5ule is mmin " @@* In our 8ase 4e assu@e t9at

m " @@*

Table ).*Stan!a&! 'a*e" #$ mn

Series $ $*# $*". $*. "*# "*. 3*# %*# .*# )*# +*# $#*# $"*#

Series " $*$". $*3-. $*-. "*". "*-. 3*. %*. .*. -*# *# $$*# $%*#

Note* Series $ s9oul5 6e ;re<erre5 to Series "

3*.* Deter@ine t9e total nu@6er o< teet9" " $)#

$)#*"

Σ× ×

= = =&a +

m

O6taine5 value o< + } s9oul5 6e roun5e5 o<< to t9e nearest inte=er

nu@eral*

3*)* Deter@ine t9e nu@6er o< teet9 o< t9e ;inion

$

pmin

+ + +

u

Σ ≥=±

:49ere + min$- <or strai=9t s;ur =ears*

O6taine5 value o< + p s9oul5 6e roun5e5 o<< to t9e nearest inte=er

nu@eral* I< + p $- it is ne8essary to 5e8rease t9e @o5ule or to use

nonstan5ar5 toot9e5 49eels* hor our 8ase

$)#"):)- $-

)$

Σ = = ≥ ==±

pmin

+ + +

u *

Roun5 o<< B ; to t9e nearest inte=er nu@eral* Assu@e B ;"-*

3*-* Deter@ine t9e nu@6er o< teet9 o< t9e =ear

$



$)# "- $33*Σ= = − = g p + + + m

U;;er si=n is ri=9t <or =ears 4it9 eternal toot9in= an5 5o4n

si=n is use5 <or =ears 4it9 internal toot9in=*

3*+* S;e8i<y t9e velo8ity ratio o< t9e =earin=

uact =

$33%:3

"-= =

g

p

+

+ .

T9e error $##mact u u

u

−×

s9oul5 6e less or eual to %m*

Ot9er4ise t9e nu@6er o< teet9 + p % + g an5 + Σ @ust 6e roun5e5 o<< to t9e ot9er

si5e*

In our 8ase 8on5ition is satis<ie5: 6e8ause%*3 .

$##m $*% %m.

−ε = × = <

3** Deter@ine t9e no@inal ;it89 8ir8les 5ia@eters <or t9e ;inion

an5 t9e =ear

d p = m, + p"j"-.% @@:

d g = 2,a&m d p"j$)#.%")) @@*

3*$#* Deter@ine t9e a55en5u@ 8ir8les 5ia@eters <or t9e ;inion

an5 t9e =ear p

ad d p ( 2,m.%z"j".+ @@: g

ad d g± 2,m"))z"j""-# @@*

3*$$* Deter@ine t9e 5e5en5u@ 8ir8les 5ia@eters <or t9e ;inion

an5 t9e =ear p

- d = d p2./,m.%"*.j"% @@:

g

- d

d g m

2./,m"))"*.j"")$ @@*3*$"* Deter@ine <or8es t9at a8t in t9e en=a=e@ent o< strai=9t s;ur

=ears7

turnin= <or8e

" " 3-#"-+$:)N

#*"))

× ×= = =

g

t g

T F

d g

ra5ial <or8e "-+$:) "# $#$":..N= × α = × ° = t & F F tg tg :

49ere ~&"#• is t9e ;ressure an=le <or t9e ;it89 8ir8le*

3*$3* Deter@ine t9e @ai@u@ 8onta8t stress t9at 5evelo;s in t9e

8onta8t Bone o< teet9

"#



( ) "

3 .

"

$$*$+

sin "

-% $# $*$$ $*"% "*$ $# %:3 $$*$+ %++:-+M€a:%:3.% +# sin %#

× × ± = × × =σ ÷

× α×

× × × × × + = × × = ÷× × °

p " t act

" g p act

&

T u $ E

ubd

49ere T p is t9e torue at t9e ;inion s9a<t in N⋅@@g $ " is t9e 5esi=n loa5

<a8tor t9at is 5eter@ine5 as $ " =$ " β⋅ $ "V : 49ere $ " β is t9e loa5

8on8entration <a8torg $ "V is t9e 5yna@i8 loa5 <a8tor*

T9e loa5 8on8entration <a8tor $ " β is s;e8i<ie5 6y ta6le 3*"

5e;en5in= u;on |bd

+#$*%+

.%

= = g

p

b

d * T9at is 49y $ " β$*$$*In or5er to 5eter@ine $ "V it is ne8essary to <in5 t9e ;eri;9eral

s;ee5 V g o< t9e =ear

%# #*")).:3"

" "

× ×ω= = = g g

g d V

@se8:

49ere g is t9e an=ular velo8ity o< t9e =ear an5 t9e =earin= a88ura8y o<

@anu<a8turin= ,ta6le 3*./*

T9e 5yna@i8 loa5 <a8tor $ "V is 5eter@ine5 6y ta6le 3*)* In our

8ase $ "V $:"%Table )./

Gea&ing a%%&a%, #$ man$a%t&ing

Ty;es o< =ear

5rives

Peri;9eral s;ee5 V : @se8

un5er . . + + $"*. over $"*.

Strai=9t s;ur =ears + - )

Heli8al s;ur =ears + -

Strai=9t 6evel =ears + -

S;iral 6evel =ears + -

Table ).0 D,nami% *#a! $a%t#& K HV

Gearin=

a88ura8y o<

@anu<a8turin=

Toot9

sur<a8e

9ar5ness:

?HN


$ " % ) + $#

- u; to 3.#

over 3.#$*#%$*#"

$*#3$*##

$*#-$*#3

$*#.$*#$

$*$%$*#.

$*#$*#"

$*"$$*#)

$*$%$*#3

$*"$*#-

$*$$*#3

$*3)$*#+

$*"%$*#%

+ u; to 3.#

over 3.#$*#%$*#$$*#3$*#$

$*#+$*#"$*#)$*#$

$*$)$*#%$*$#$*#"

$*"%$*#)$*$)$*#3

$*3"$*#-$*""$*#%

$*%#$*#+$*")$*#.

u; to 3.# $*#.$*#$ $*$#$*#3 $*"#$*#. $*3#$*#- $*%#$*# $*.#$*$"

"$



over 3.# $*#%$*#$ $*#-$*#$ $*$3$*#" $*"#$*#3 $*")$*#% $*3"$*#.

Note7 T9e <i=ures in t9e nu@erators re<er to strai=9t s;ur =ears an5 t9ose in t9e

5eno@inators: to 9eli8al s;ur =ears*

O6taine5 value o< w " s9oul5 8orres;on5 to t9e 8on5ition7

w " ,#*+$*$/jw " x*

Ot9er4ise it is ne8essary to 89an=e t9e 8enter 5istan8e a4 an5

re8al8ulate t9e =earin=*

In our 8ase %$":%%++:-+.)-* Con5ition is satis<ie5*

3*$%* Deter@ine t9e @ai@u@ 6en5in= stress

"-+$:) $*") $*.+ 3*)$"%*)$MPa x "..:)MPa

" +#

β× × × × × ×σ = = = ≤ =σ

××t b bbV

bb g

$ F $ 1

m b

49ere $ bβ is t9e loa5 8on8entration <a8tor t9at is 5eter@ine5 6y ta6le 3*-g

$ b is t9e 5yna@i8 loa5 <a8tor 5eter@ine5 <ro@ ta6le 3*+g b is t9e toot9

<or@ <a8tor t9at is 5eter@ine5 6y @eans o< ta6le 3* 5e;en5in= u;on t9e

nu@6er o< teet9 o< t9e =ear <or t9e 8ase 49en t9e o<<set <a8tor 3#*

I< o6taine5 @a=nitu5e o< wbwbx it is ne8essary to in8rease t9e @o5ule*

Table ).4 A++&#imate 'a*e" #$ K b4

Gear arran=e@ent

4it9 res;e8t to 6earin=s

Toot9 sur<a8e

9ar5ness:?HN

g

bd p

b

d ψ =#*" #*% #*) #*+ $*" $*)

On 8antilevers:

6all 6earin=s

u; to 3.#

over 3.#

$*$)

$*33

$*3-

$*-#

$*)%

On 8antilevers:roller 6earin=s

u; to 3.#over 3.#

$*$#$*"#

$*""$*%%

$*3+$*-$

$*.-

Sy@@etri8alu; to 3.#

over 3.#

$*#$

$*#"

$*#3

$*#%

$*#.

$*#+

$*#-

$*$%

$*$%

$*3#

$*")

Nonsy@@etri8alu; to 3.#

over 3.#

$*#.

$*#

$*$#

$*$+

$*$-

$*3#

$*".

$*%3

$*%"

$*-3

$*)$

Table ).5

D,nami% *#a! $a%t#& K bV

Gearin=

a88ura8y o< @anu<a8turin=

Toot9

sur<a8e9ar5ness:

?HN


$ " % ) + $#

- u; to 3.#

over 3.#

$*#+$*#

3$*#3$*#

$

$*$)$*#

)$*#.$*#

"

$*33$*$$

$*#$*#3

$*.#$*$

)$*$3$*#

.

$*)"$*"

"$*$-$*#

-

$*+#$*"

-$*""$*#

+

""



+ u; to 3.#over 3.#

$*$#$*#3

$*#%$*#

$

$*"#$*#)

$*#)$*#

"

$*3+$*$$$*$"$*#

3

$*.+$*$-

$*$)$*#

.

$*-+$*"3

$*"$$*#

.

$*)$*"

$*")$*#

+

u; to 3.#over 3.#

$*$3$*#%

$*#%$*#

$

$*"+$*#-

$*#-$*#

"

$*.#$*$%

$*$%$*#

%

$*-"$*"$

$*"$$*#

)

$*+$*"+

$*"-$*#

+

$*".$*3.

$*3%$*#

Note7 T9e <i=ures in t9e nu@erators re<er to strai=9t s;ur =ears an5 t9ose in t9e

5eno@inators: to 9eli8al s;ur =ears*

Table ).6T##th $#&m $a%t#& Y b

+ or + $- "# "" "% ") "+ 3# 3. %# %. .# ). +# $##

6 %*"- %*#- 3*+ 3*" 3*++ 3*+$ 3*+ 3*-. 3*- 3*)) 3*). 3*)" 3*)$ 3*)

5. ANALSIS O/ THE HELICAL SPUR GEARS /OR

STRENGTH

%*$* Deter@ine t9e 8enter 5istan8e o< t9e 9eli8al s;ur =ears

( )=

H tr 3

4 " "H 6a

T K E#*-. u $

x ua

β× ×= × + ×

× ×σ ψ :

49ere u is t9e velo8ity ratio o< t9e =earin=g T g

is t9e torue at t9e =ear s9a<t in 78mmg 9 " x is t9e allo4a6le 8onta8t stress in MPag Etr is t9e

trans<or@e5 @o5ulus o< elasti8ity in MPag $ ": is t9e loa5 8on8entration

<a8torg | 6a 6=a4 is t9e =ear <a8e 4i5t9 <a8tor*

Trans<or@e5 @o5ulus o< elasti8ity E t is 5eter@ine5 as ; =

tr ; =

" E EE

E E

× ×=

+ :

49ere E p an5 E g are 8orres;on5in=ly @o5ules o< elasti8ity o< ;inion

an5 =ear @aterials* Sin8e t9e ;inion an5 t9e =ear are @a5e o< steel 4e8an @a>e t9e 8on8lusion t9at Etr E ; E= "*$j$#. MPa*

Loa5 8on8entration <a8tor $ ": is 5eter@ine5 6y @eans o< ta6le 3*"

5e;en5in= on 5is;osition o< toot9e5 49eels 4it9 res;e8t to 6earin=s an5

<a8tor | 65 6=5 ;* Sin8e 6= an5 5 ; 4ere not 5eter@ine5 4e <in5 t9is <a8tor

6y t9e <ollo4in= <or@ula

( ) ( )= =

65 6a ;4

#*. 6 6u $ #*. u $

5 a

×ψ = = × ± = × ψ × ±

:

"3



49ere =ear <a8e 4i5t9 <a8tor | 6a is 5eter@ine5 <ro@ ta6le 3*$ 5e;en5in=

on t9e 5is;osition o< t9e =ear relative to 6earin=s ta>in= into a88ount

t9at t9e value o< t9is <a8tor s9oul5 8orres;on5 to stan5ar5* T9e =reater

| 6a 8orres;on5s to t9e less overall 5i@ensions o< t9e =earin=* T9at is49y 4e sele8t t9e =reater @a=nitu5e o< | 6a*

O6taine5 @a=nitu5e o< a& s9oul5 6e roun5e5 o<< to t9e nearest

=reater si5e a88or5in= to t9e series =iven in ta6le 3*3*

In our 8ase7 T= %)%*3 Nj@g T ; $$*)- Nj@g u %g

wHx .$.:. MPa6 Etr "*$j$#. MPa6 w 6x "..*) MPa: sy@@etri8al

5is;osition o< =ears 4it9 res;e8t to su;;orts*

hro@ ta6le 3*$ 4e ta>e | 6a #*.g t9en( ) 65 #*. #*. % $ $*".ψ = × × + =

:

hro@ ta6le 3*" 4e ta>e K H{ $*#- ,<or sy@@etri8al =ear arran=e@ent an5 toot9 sur<a8e 9ar5ness u; to 3.#/*

T9en

( ).

34 " "

%)%3## $*#- "*$ $##*-. % $ $3-*"@@

#*..$.*. %

× × ×= × + × =

× ×a

Roun5 o<< o6taine5 @a=nitu5e to t9e nearest =reater si5e a88or5in=

to ta6le 3*3* T9at is 49y 4e ta>e a& = $%# mm <or <urt9er 8al8ulations.

%*"* Deter@ine t9e no@inal ;it89 8ir8le 5ia@eter o< t9e =ear

4= " u " $%# %

""%@@5u $ % $

× × × ×= = =

+ +a

*

%*3* Deter@ine t9e <a8e 4i5t9 o< t9e =ear

6= | 6aja4 #*.j$%# -# @@*

%*%* Deter@ine t9e nor@al @o5ule a88or5in= to t9e stren=t9

8on5ition <or 6en5in==

@

n = =

6

" K T@

5 6 x

⋅ ⋅≥

⋅ ⋅ σ:

49ere K @ is ta>en as .*+ <or 9eli8al s;ur =ears*

O6taine5 @a=nitu5e o< t9e @o5ule s9oul5 6e roun5e5 o<< to t9e

=reater si5e a88or5in= to t9e stan5ar5 series =iven in ta6le 3*%* It is

ne8essary to note t9at <or =eneral;ur;ose s;ee5 re5u8ers t9e @ini@u@

value o< t9e @o5ule is @@in " @@* In our 8ase

"%



n

" .*+ %)%3##@ $*3%%@@

""% -# "..*)

× ×= =

× × %

4e ta>e mn = 2 @@ <or <urt9er 8al8ulations*

%*.* Deter@ine t9e 9eli an=le

n

=

3:. @ 3:. "ar8sin ar8sin .*-3

-# 6

× × β = = = ° ÷ ÷ *

hor 9eli8al s;ur =ears t9is an=le s9oul5 6e ran=e5 <ro@ + to $+•*

Ot9er4ise: it is ne8essary to 89an=e t9e nor@al @o5ule @ n* As in our

8ase .*-3= oβ t9at is less t9an +o

: 4e ta>e mn=3 @@* T9en

3*. 3ar8sin +*)" *

-#

× β = = ° ÷

%*)* Deter@ine t9e total nu@6er o< teet9

4

n

" 8os " $%# 8os +*)""*"+B

@ 3Σ

× × β × ×= = =a

o

*

O6taine5 value o< B} s9oul5 6e roun5e5 o<< to t9e nearest inte=er

nu@eral: assu@e B} "*

%*-* S;e8i<y t9e 9eli an=le a88or5in= to t9e inte=er nu@6er o< B}

n

4

@ B 3 "ar88os ar88os *)

" " $%#

Σ × × β = = = ÷ ÷× × a

o

O6taine5 value o< t9is an=le is ran=e5 <ro@ + to $+•* Con5ition is

satis<ie5*

%*+* Deter@ine t9e nu@6er o< teet9 o< t9e ;inion

;@in

BBB

u $

Σ ≥=± :

49ere <or 9eli8al s;ur =ears B@in$-q38os β *

O6taine5 value o< B ; s9oul5 6e roun5e5 o<< to t9e nearest inte=er

nu@eral* I< B ; $-q38os β it is ne8essary to 5e8rease t9e @o5ule or to use

nonstan5ar5 toot9e5 49eels*In our 8ase

".



; 3 ;@in

"$+*% B $+ B $- 8os *) $)*"+*B

% $= ⇒ = > = × ==

±o

%** Deter@ine t9e nu@6er o< teet9 o< t9e =ear = ;

B B B " $+ -%Σ= − = − =*

%*$#* S;e8i<y t9e velo8ity ratio o< t9e =earin=

ua8t

=

;

B

B *

T9e error

a8tu u

$##mu

−×


Ot9er4ise t9e nu@6er o< teet9 B ;: B= an5 B} @ust 6e roun5e5 o<< to t9e

ot9er si5e*

In our 8ase 8on5ition is satis<ie5: sin8e

a8t

-%u %*$$

$+= =

g

%*$$ %$##m "*-. %m

%

−ε = × = <

%*$$* Deter@ine t9e no@inal ;it89 8ir8le 5ia@eters <or t9e ;inion an5

t9e =ear

; ;n@ 3

5 B $+ .%*-+@@8os 8os:)

= × = × =β o

:

5= "qa4 5 ; "q$%# .%*-+ "".*"" @@*

%*$"* Deter@ine t9e a55en5u@ 8ir8le 5ia@eters <or t9e ;inion an5

t9e =ear

; ;

a n5 5 "@ .%*-+ " 3 )#*-+@@= + = + × =:

= =

a n5 5 "@ "".*"" " 3 "3$*""@@= + = + × = *

%*$3* Deter@ine t9e 5e5en5u@ 8ir8le 5ia@eters <or t9e ;inion an5

t9e =ear

; ;

< n5 5 "*. @ .%*-+ "*. 3 %-*"+@@= − × = − × = :

= =

< n5 5 "*. @ "".*"" "*. 3 "$-*-"@@= − × = − × =*

")



%*$%* Deter@ine <or8es t9at a8t in t9e en=a=e@ent o< t9e 9eli8al s;ur

=ears7

turnin= <or8e

=

t

=

" T " %)%3##%$"3*#+Nh

"".*""5

× ×= = =

g

ra5ial <or8e

t

r 4

h %$"3*#+h t= t="# $.""*%N

8os 8os*)= × α = × =

βo

o

g

aial <or8e a th h t= %$"3*#+ t=*) -#%*#3N:= × β = × =o

49ere ~4"#• is t9e ;ressure an=le <or t9e ;it89 8ir8le*

%*$.* Deter@ine t9e @ai@u@ 8onta8t stress t9at 5evelo;s in t9e


( )

;H tr a8t

H H "= ; a8t

4

T $uK E$*$+ •

usin" 65β

× × ± = × × ×σ ÷

× α×:

49ere H{ is a <a8tor 49i89 is use5 to ta>e into a88ount risin= t9e 8onta8t

stren=t9 o< t9e 9eli8al s;ur =ears in 8o@;arison 4it9 t9e strai=9t s;ur

=earsg T ; is t9e torue at t9e ;inion s9a<t in 78mmg $ " is t9e 5esi=n loa5

<a8tor t9at is 5eter@ine5 as

" " "V $ $ $ β = ×:

49ere K H{ is t9e loa5 8on8entration <a8torg K H! is t9e 5yna@i8 loa5

<a8tor*

T9e loa5 8on8entration <a8tor K H{ is s;e8i<ie5 6y ta6le 3*" 5e;en5in=

u;on

=

65 ;

6

5

ψ =

*In or5er to 5eter@ine K H! it is ne8essary to <in5 t9e ;eri;9eral s;ee5

!= o< t9e =ear = =

= 5!

"

×ω=

49ere = is t9e an=ular velo8ity o< t9e =ear an5 t9e =earin= a88ura8y o<

@anu<a8turin= ,ta6le 3*./:*

T9e 5yna@i8 loa5 <a8tor K H! is 5eter@ine5 6y ta6le 3*)*

ha8tor H{ is 5eter@ine5 in t9e <ollo4in= 4ay

"-



"

HH

K 8os• α

βα

× β=

ε:

49ere K H~ ta>es into a88ount nonuni<or@ loa5 5istri6ution 6et4eenseveral ;airs o< teet9g ~ is t9e 8onta8t ratio*

Table *.1/a%t#&" 7 H8 9 7 08 hi%h a&e "e! t# tae int# a%%#nt n#n;ni$#&m *#a!

!i"t&i0ti#n 0eteen "#me +ai&"

Peri;9eral s;ee5

!: @se8

A88ura8y o<

@anu<a8turin

=

K H~ K 6~

To . - $*#3 $*#-

+ $*#- $*"" $*$3 $*3.

hro@ . to $# - $*#. $*"

+ $*$# $*3

hro@ $# to $. - $*#+ $*".

+ $*$. $*%#

K H~ 5e;en5s u;on t9e a88ura8y o< @anu<a8turin= an5 t9e ;eri;9eral

s;ee5 an5 is 5eter@ine5 a88or5in= to ta6le %*$*

Conta8t ratio ~ is <oun5 6y t9e <ollo4in= <or@ula

; =

$ $$*++ 3*" 8os

B Bα

ε = − × + × ÷ *

Let us 5eter@ine t9e 8onta8t stress w " <or our 8ase7

65

-#$*"-

.%*-+ψ = =

; K H{ $*#-g

=H!

$*$ #*""."""*$)@ se8 K $*#$!

"

×= = ⇒ =

g

A88ura8y o< @anu<a8turin= o< t9e =earin= is ; $ " $*#-j$*#$

$*#+#-g

$ $$*++ 3*" 8os*) $*)3.

$+ -%α

ε = − × + × ° = ÷ ; $ "< = 1.1);"

H

$*$3 8os *)• #*+$

$*)3.β

×= =

o

g

"+



H "

$$)-# $*#+#- "$#### %*$$ $$*$+ #*+$ %+3*"+-MPa

%*$$-# sin," "# /.%*-+

× × + = × × × =σ ÷× × × o

g

O6taine5 value o< w " s9oul5 8orres;on5 to t9e <ollo4in=

8on5ition7

w " ,#*+$*$/jw " x*



In our 8ase %$":%%+3:"+-.)-* Con5ition is satis<ie5*

%*$)* Deter@ine t9e @ai@u@ 6en5in= stress

t 6 6 6! 6

6 6 =

n

K •h K

x@ 6

β β× × × ×σ = ≤ σ× :

49ere K 6{ is t9e loa5 8on8entration <a8tor t9at is 5eter@ine5 6y ta6le

3*-g K 6v is t9e 5yna@i8 loa5 <a8tor 5eter@ine5 <ro@ ta6le 3*+g 6 is t9e

toot9 <or@ <a8tor t9at is 5eter@ine5 6y @eans o< ta6le 3* 5e;en5in= on

t9e nu@6er o< teet9 o< t9e euivalent strai=9t s;ur =ear

==

v 3

BB

8os=

β <or

t9e 8ase 49en t9e s9i<t <a8tor #*ha8tor 6{ is t9e analo=y o< H{ an5 is 5eter@ine5 as

6

6

K •

α ββ

α

×=

ε:

49ere K 6~ is 89osen <ro@ ta6le %*$g $

$%#β

β= −

o

is t9e 8orre8tion <a8tor*

I< o6taine5 @a=nitu5e o< w 6 w 6x it is ne8essary to in8rease t9e

@o5ule*

In our 8ase7 K 6{ $*$%g K 6v $*#-g

=

v 3

-%B --*")

8os *)= =

o

g

6 3*)$g K 6~ $*3.g

*) $ #*3

$%#β = − =

o

g 6

$*3. #*3• #*-)+

$*)3.β

×= =

g

6 6

%$"3*#+ $*$% $*#- #*-)+ 3*)$))*%MPa x"..*)MPa

3 -#

× × × ×σ = = < σ

× *

Stren=t9 8on5ition is satis<ie5.

"



<. ANALSIS O/ THE )E=EL GEARS /OR STRENGTH

Let us analyse t9e 6evel =ears <or stren=t9 i< torue at t9e ;inion

s9a<t T p

%)# N⋅@g torue at t9e =ear s9a<t T g

$.3 N⋅@ velo8ity ratio o< t9e =earin= u3*$.g allo4a6le 8onta8t stress w " x)%# MPag allo4a6le

6en5in= stress wbx"3 MPa: 9ar5ness o< t9e =ear @aterial " g "+.

?HN*

.*$* Deter@ine t9e eternal ;it89 5ia@eter o< t9e =ear

[ ]3

"$*-

,$ /

g " t g

e

" " b b

T u $ E d

β× × ×= ×

× × × −ψ ψ ν σ:

49ere T g is t9e torue at t9e =ear s9a<t in Nj@@g E t is t9e trans<or@e5@o5ulus o< elasti8ityg $ " { is t9e loa5 8on8entration <a8torg u is t9e

velo8ity ratiog ‚ " #*+. is t9e 8orre8tion <a8tor t9at ta>es into a88ount

re5u8in= 6evel =ears stren=t9 in 8o@;arison 4it9 s;ur =earsg w " x is t9e

allo4a6le 8onta8t stressg |bb g 'e is t9e =ear <a8e 4i5t9 <a8tor t9at

5eter@ines ;ro;ortions o< t9e <a8e 4i5t9 o< t9e =ear 4it9 res;e8t to t9e

eternal 8one 5istan8e* ha8tor |b @ust 6e less t9an #*3* Re8o@@en5e5

value o< |b #*"+.*

Sin8e 6ot9 ;inion an5 =ear are @a5e o< steel: t9e trans<or@e5@o5ulus o< elasti8ity E t "*$q$#. MPa*

Loa5 8on8entration <a8tor $ " { 5e;en5s u;on t9e 9ar5ness o< t9e

=ear @aterial* I< " g ≤3.# ?HN $ " { is ran=e5 <ro@$*"3 to $*3.* Ot9er4ise

, " g 3.# ?HN/ $ " { is ran=e5 <ro@ $*". to $*%.* It is ne8essary to note

t9at =reater values o< $ " { are assu@e5 <or t9e 8ase 49en one o< toot9e5

49eels is on t9e 8antilever s9a<t*

[ ]

3 .

33 " "

%)# $# $*3 "*$ $# 3*$.

$*- $:- 3#$*%.@@*#*+. )%# #*"+. ,$ #*"+./,$ /

β× × × × × × × ×= × = × =× × × −× × × −ψ ψ ν σ

g " t g

e

" " b b

T u $ E d

A<ter 8al8ulation t9e o6taine5 @a=nitu5e o< g

ed s9oul5 6e

roun5e5 o<< to t9e =reater si5e a88or5in= to stan5ar5 series =iven in

ta6le .*$* In our 8ase 4e assu@e g

ed 3$. @@*

3#



Table /.1

Stan!a&! 'a*e" #$ the ete&na* +it%h !iamete& g

ed

Series $ %# .# )3 +# $## $". $)# "## ".# 3$. %## .##

Series " -$ # $$" $%# $+# ""% "+# 3.. %.# .)#

.*"* Deter@ine ;it89 an=les <or t9e ;inion an5 <or t9e =ear*

δ" ar8t= u ar8t= 3*$.-"*3+ƒ: δ$ #° δ"#-"*3+$-*)"ƒ*

.*3* Deter@ine t9e eternal 8one 5istan8e

"

3$.$).*".@@

" sin " sin-"*3+= = =

× δ × °

g

e

e

d

*

.*%* Deter@ine t9e <a8e 4i5t9 o< t9e =ear

b g bψ ⋅ e#*"+.j$).*".%-*$ @@*

.*.* Deter@ine t9e eternal @o5ule3

=

e

$% $% %)# $# $:3."*3.@@

#*+. 3$. %-*$ "35 x

β× × × × ×= = =

× × × ν × × × σ

g

b

e g

b b

T $ m

b:

49ere ‚b #*+. is t9e 8orre8tion <a8torg $ b{ is t9e loa5 8on8entration

<a8tor t9at is 5eter@ine5 a88or5in= to ta6le 3*- 5e;en5in= u;on |bd

<a8tor: 49ere t9e latter is <oun5 as

" "#*$)) $ #*$)) 3*$. $ #*..×ψ = = × + = × + = g

bd p

m

bu

d *

.*)* Deter@ine t9e nu@6er o< teet9 o< t9e =ear

= 3$.B $3%*#%"*3.= = =

g

e

e

d

m

an5 roun5 o<< g + to t9e inte=er nu@eral* Assu@e $3%= g

+ *

.*-* Deter@ine t9e nu@6er o< teet9 o< t9e ;inion

$3%%"*.%

3*$.= = =

g p +

+ u

an5 roun5 o<< p + to t9e inte=er nu@eral too* In our 8ase %3*= p +

.*+* S;e8i<y t9e velo8ity ratio o< t9e =earin=

3$



uact

$3%3*$"

%3= =

g

p

+

+ *

T9e error $##m

act u u

u

−×


Ot9er4ise: 4e s9oul5 roun5 o<< values o< + p an5 + g to t9e ot9er si5e*

In our 8ase

$##mact u u

u

−×

3*$" 3*$.$##m #*. %m*

3*$.

−× = <

.** S;e8i<y ;it89 an=les <or t9e ;inion an5 t9e =ear

δ" ar8t= uact ar8t= 3*$"-"*"3ƒ: δ$ #° δ"$-*--ƒ

.*$#* Deter@ine eternal ;it89 5ia@eters o< t9e ;inion an5 t9e

=ear*

"*3. %3 $#$*#.@@= × = × = p p

e ed m + :

=

e5 "*3. $3% 3$%*@@= × = × = g

em + *

.*$$* Deter@ine 5ia@eters o< a55en5u@ 8ir8les at t9e outer

se8tion <or t9e ;inion an5 t9e =ear

$" 8os p p

ae e ed d m= + × × $#$*#.z"j"*3.j8os$-*--ƒ$#.*.3 @@:

"" 8os g g

ae e ed d m= + × × δ3$%*$z"j"*3.j8os-"*"3ƒ3$)*33 @@*

.*$"* Deter@ine 5ia@eters o< 5e5en5u@ 8ir8les at t9e outer

se8tion <or t9e ;inion an5 t9e =ear*

$"*% 8os p p

-e e ed d m= − × ×$#$*#."*%j"*3.j8os$-*--ƒ.*)+ @@:

""*% 8os g g

-e e ed d m= − × × δ3$%*"*%j"*3.j8os-"*"3ƒ3$3*$+ @@*

.*$3* S;e8i<y t9e eternal 8one 5istan8e

( ) ( )" "

" "#*. #*. "*3. %3 $3% $).*3)@@= × × + = × × + = p g e e + + m

*

.*$%* S;e8i<y t9e <a8e 4i5t9 o< t9e =ear g

b eb = ψ × #*"+.j$).*3)%-*"+ @@*

3"



.*$.* Deter@ine @ean ;it89 5ia@eters <or t9e ;inion an5 <or t9e

=ear

( ), #*. /

$ #*. $#$*#. ,$ #*. #*"+./ +)*).@@× − ×

= = × − ×ψ = × − × = p g

p pe e

m e b

e

d bd d

:

( ), #*. /

$ #*. 3$%* ,$ #*. #*"+./ "-#*#3@@× − ×

= = × − ×ψ = × − × = g g

g g e e

m e b

e

d bd d

*

.*$)* Deter@ine <or8es t9at a8t in t9e en=a=e@ent o< t9e 6evel

=ears

turnin= <or8e3

" " %)# $#3%#-*#3N"-#*#3

× × ×= = =

g

t g

m

T F d

g

ra5ial <or8e at t9e =ear

"8os g

t & F F tg = × α × δ3%#-*#3jt="#ƒj8os-"*"3ƒ3-+*%) Ng

aial <or8e at t9e =ear

"sin g

a t & F F tg = × α × δ3%#-*#3jt="#ƒjsin-"*"3ƒ$$+#*+ N*

.*$-* Deter@ine t9e @ai@u@ 8onta8t stress t9at 5evelo;s in t9e


( )

"

"

3 . "

"

$$*$+

sin "

$.3 $# $*" "*$ $# 3*$" $$*$+ ..+*+MPa:

3*$"#*+. +)*). %-*"+ sin %#

+× × ÷σ = × × = ÷ ν × × × α

× × × × + ÷= × × =

÷× × × °

pact " t

" p g

act " m &

uT $ E

ud b

49ere T p is in Nq@@g $ " is t9e 5esi=n loa5 <a8tor 5eter@ine as

$ " =$ " {q $ "V *

Loa5 8on8entration <a8tor K H{ is s;e8i<ie5 6y @eans o< ta6le 3*"

5e;en5in= u;on <a8tor | 65

g

p

m

b

d *

33



Dyna@i8 loa5 <a8tor $ "V is 5eter@ine5 a88or5in= to ta6le 3*)

5e;en5in= u;on t9e ;eri;9eral s;ee5 o< t9e =ear ,V g "

g g

md ω ×

/ an5 t9e

a88ura8y o< @anu<a8turin= ,ta6le 3*./* In or5er to use ta6le 3*) <or 6evel=ears 4e s9oul5 re5u8e t9e 5e=ree o< a88ura8y 6y $*

In our 8ase |bd

%-*"+#*..

+)*).= =

g

p

m

b

d : V =

". #*"-3*%

" "

g g

md ω × ×= =

@se8*

$ " =$ " {q $ "V $*$)j$*$$$*"*

O6taine5 value o< w " s9oul5 8orres;on5 to t9e <ollo4in=

8on5ition

w " ,#*+$*$/qw " x,#*+$*$/q)%#.$"-#% MPa*

Ot9er4ise it is ne8essary to 89an=e t9e eternal ;it89 5ia@eter

an5 re8al8ulate t9e =earin=* In our 8ase stren=t9 8on5ition is satis<ie5*

.*$+* Deter@ine t9e @ai@u@ 6en5in= stress

3%#-*#3 $*3" $*"- 3*)".3*"+MPa x "3MPa

#*+. "*#" %-*"+

β× × × × × ×σ = = = ≤ =σ

× × ν × ×t b bbV

bb g

b m

$ F $

m b

49ere $ bβ is t9e loa5 8on8entration <a8tor t9at is 5eter@ine5 6y ta6le3*-g $ bV is t9e 5yna@i8 loa5 <a8tor 5eter@ine5 <ro@ ta6le 3*+ ,<or 6evel

=ears 4e s9oul5 re5u8e t9e a88ura8y o< @anu<a8turin= 6y $/g b is t9e

toot9 <or@ <a8tor t9at is 5eter@ine5 6y @eans o< ta6le 3* 5e;en5in=

u;on t9e nu@6er o< teet9 o< t9e euivalent strai=9t s;ur =ear

"

$3%%3

8os 8os-"*"3ƒ= = =

δ

g g

+ +

<or t9e 8ase 49en t9e o<<set <a8tor 3#g

‚b #*+. is t9e 8orre8tion <a8torg mm"-#*#3 "*#"@@

$3%= =

g

m

g d + is t9e @ean

@o5ule*

3%



>. ANALSIS O/ THE (ORM GEARING

Let us 8arry out t9e analysis o< t9e 4or@ =earin= <or stren=t9 i<

torue at t9e 4or@ s9a<t T &

=1>/ N⋅@g torue at t9e =ear s9a<t T g

= 14/> N⋅@g rotational s;ee5 o< t9e 4or@ s9a<t n& %%$*-. r;@: rotational

s;ee5 o< t9e =ear s9a<t n g ""*$ r;@; velo8ity ratio o< t9e =earin= u"#*

)*$* Deter@ine a;;roi@ately t9e sli;;a=e s;ee5 in t9e 4or@

=earin=3% 4 =

sl! %*. $# n T−= ⋅ ⋅ ⋅ :

49ere n& is t9e rotational s;ee5 o< t9e 4or@ in r;@g T g is t9e torue at

t9e 4or@ =ear s9a<t in Nq@*% 3

sl! %*. $# %%$*-. $-.# "*%@ A se8−= × × × =

)*"* Sele8t t9e @aterial o< t9e 4or@ an5 t9e 4or@ =ear*

(#&m

T9e 6est ;er<or@an8e is o6taine5 49en 4or@s are @a5e o< 8ar6on

or alloy steels o< =ra5e Steel %. ,#*%. C/ an5 Steel %#pH ,#*%#CCr

Ni/ sur<a8e9ar5ene5 to 9ar5ness ran=e5 <ro@ .# to .. HRC or o< =ra5e

Steel "#p ,#*"# CCr/ an5 Steel $+p„ ,#*$+ CCrMnTi/ 8ase

9ar5ene5 to 9ar5ness ran=e5 <ro@ .+ to )3 HRC* T9e i@@unity to

seiBure i@;roves 4it9 in8reasin= 9ar5ness o< t9e 4or>in= sur<a8es o<

t9rea5s* Also: t9e sur<a8e rou=9ness o< t9e t9rea5s s9oul5 6e >e;t to a

@ini@u@ ,usually a >.2/* hor t9is ;ur;ose t9e t9rea5s are =roun5 an5

;olis9e5*

(#&m gea&

Material o< t9e 4or@ =ear 5e;en5s on t9e sli;;a=e s;ee5*

I< !sl. @se8: t9e 4or@ =ear is @a5e o< tin 6ronBes su89 as

?ronBe$#Sn$Ni$P: ?ronBe$#Sn$P*

I< !sl is ran=e5 <ro@ " to . @se8: t9e 4or@ =ear is @a5e o< tinless

,alu@inu@iron/ 6ronBes su89 as ?ronBeAl%he*

I< !sl" @se8: t9e 4or@ =ear is ;ro5u8e5 <ro@ 8ast irons su89 as

Grey 8ast iron $" or Grey 8ast iron $+*

Me89ani8al 89ara8teristi8s o< @aterials o< t9e 4or@ =ear are =iven

in ta6le )*$* It is re8o@@en5e5 to 89oose t9e @aterial o< t9e 4or@ =ear

4it9 9i=9er @e89ani8al 89ara8teristi8s*

It is ne8essary to note t9at 8al8ulation o< t9e 4or@ =earin= is 8arrie5

3.



out 6y t9e @aterial o< t9e 4or@ =ear 6e8ause t9e latter 9as less stren=t9

in 8o@;arison 4it9 t9e @aterial o< t9e 4or@*

In our 8ase7 4or@ is @a5e o< 8ar6on steels o< =ra5e Steel %. ,#*%. C/

an5 sur<a8e9ar5ene5 to 9ar5ness ran=e5 <ro@ .# to .. HRCg t9e 4or@=ear is @a5e o< tinless ,alu@inu@iron/ 6ronBes su89 as ?ronBe Al%he

4it9 89ill 8astin= to σy $. MPa: ulti@ate stren=t9 in tension σult %#

MPa*

Table 0.1Me%hani%a* %ha&a%te&i"ti%" #$ mate&ia*" #$ the #&m gea& &ing

Material

Sli;;a=e

s;ee5 !s:

@se8

Castin= @et9o5

Me89ani8al 89ara8teristi8s:

MPa

iel5

;oint

σy

Ulti@ate stren=t9

in tension

σul t

in 6en5in=

σul 6

Tin 0&#n?e"

?ronBe,$#Sn$Ni

$P/Over .

Centri<u=al

8astin=$). "+.

?ronBe,$#Sn$P/ Over . C9ill 8astin= $. "%.

?ronBe,$#Sn$P/ Over . San5 8astin= $3" "$.

Tin*e"" 0&#n?e"?ronBe,Al%he/ ".

Centri<u=al

8astin="## .##

?ronBe,Al%he/ ". C9ill 8astin= $. %#

?ronBe,Al%he/ ". San5 8astin= $. 3"

Ca"t;i&#n"

Grey 8ast iron $" U; to " San5 8astin= "+#

Grey 8ast iron $+ U; to " San5 8astin= 3)#

)*3* Deter@ine t9e allo4a6le 8onta8t stress*

a/ hor t9e 4or@ =ear @a5e o< tin 6ronBes t9e allo4a6le 8onta8t

stress is 5eter@ine5 <ro@ t9e 8on5ition to ;revent <ati=ue ;ittin=

σHx σli@qCvqK HL:

49ere σli@ is t9e li@it o< 8onta8t en5uran8e t9at is 5eter@ine5 as σli@

#*qσultg σult is t9e ulti@ate stren=t9 in tension ,ta6le )*$/g Cv is t9e <a8tor

t9at is use5 to ta>e into a88ount t9e 4ear rate o< a 4or@ =ear toot9

5e;en5in= u;on t9e sli;;a=e s;ee5 ,ta6le )*"/g K HL is t9e 5ura6ility <a8tor*

3)



Table 0.2=a*e" #$ C'

Sli;;a=e s;ee5 !sl: @se8 . ) - +

Cv #*. #*++ #*+3 #*+

Dura6ility <a8tor K HL is <oun5 in t9e <ollo4in= 4ay7

H#+

HL

Hi

NK

N=

:

49ere NHO $#- is t9e 6ase nu@6er o< 8y8lesg

NHi )#qn=qt is t9e 5esi=n nu@6er o< stress 8y8lesg

n=

is t9e rotational s;ee5 o< t9e 4or@ =eargt L⋅3).⋅K a⋅"%⋅K 5 is t9e servi8e li<e in 9oursg

L is t9e servi8e li<e in yearsg K a is t9e annual utiliBation <a8torg K 5 is

t9e 5aily utiliBation <a8torg

O6taine5 @a=nitu5e o< K HL s9oul5 satis<y t9e <ollo4in= 8on5ition7

#*)- K HL$*$.*

Ot9er4ise: <or <urt9er 8al8ulations 4e ta>e t9e etre@e values o< t9e

@entione5 a6ove ineuality* 6/ hor t9e 4or@ =ear @a5e o< eit9er tinless 6ronBes or 8ast irons: t9e

allo4a6le 8onta8t stress is 5eter@ine5 to avoi5 seiBure7

<or tinless 6ronBes σHx 3## ".j!slg

<or 8ast iron σHx $-. 3.j!sl*

In our 8ase7 σHx 3## ".j"*% "%# MPa

)*%* Deter@ine t9e allo4a6le 6en5in= stress*

hor t9is ;ur;ose 4e use ta6le )*3: 49ere σul t is t9e ulti@ate stren=t9

in tensiong σul 6 is t9e ulti@ate stren=t9 in 6en5in=g σy is t9e yiel5 ;ointg

K 6L is t9e 5ura6ility <a8tor*

Table 0.)A**#a0*e 0en!ing "t&e""e"

Material Nonreverse5 trans@ission Reverse5 trans@ission

?ronBe w 6x ,#*#+qwul t z #*".qwy/qK 6L w 6x #*$)qwul tqK 6L

Cast

ironw 6x #*$"qwul 6qK 6L w 6x #*#-.qwul 6qK 6L

3-



Me89ani8al 89ara8teristi8s o< t9e 4or@ =ear @aterial are =iven in

ta6le )*$*

Dura6ility <a8tor K 6L is 5eter@ine5 as

6# 6L

6i

NK N

=:

49ere N 6# $j$#) is t9e 6ase nu@6er o< 8y8lesg

N 6i )#qn=qtqK 6i is t9e 5esi=n nu@6er o< stress 8y8lesg

n= is t9e rotational s;ee5 o< t9e 4or@ =earg

t L⋅3).⋅K a⋅"%⋅K 5 is t9e servi8e li<e in 9oursg

L is t9e servi8e li<e in yearsg K a is t9e annual utiliBation <a8torg K 5 is

t9e 5aily utiliBation <a8torgO6taine5 @a=nitu5e o< K 6L s9oul5 satis<y t9e <ollo4in= 8on5ition7

#*.%3 K 6L$*

Ot9er4ise: <or <urt9er 8al8ulations 4e ta>e t9e etre@e values o< t9e

@entione5 a6ove ineuality*

In our 8ase t9e servi8e li<e o< t9e =earin= is + years: K a #*-:

K 5 #*3:

+ 3). #*- "% #*3 $%-$)*+9ourst = × × × × = * N 6i )#q""*$q$%-$)*+ $*$%%j$#)g N 6# $j$#)g

)

6L )

$ $##*-$K

$*$%% $#

×= =

× Con5ition #*.%3 K 6L$ is satis<ie5*

hor 6ronBe an5 nonreverse5 trans@ission

w 6x ,#*#+q%# z #*".q$./q#*-$ )3*"% MPa

)*.*Cal8ulate t9e 4or@ =ear <or stren=t9*

)*.*$* Deter@ine t9e 8enter 5istan8e o< t9e 4or@ =earin=

4 =tr

4 = 43 "

H =

T E#*)". $

B x

B

⋅= ⋅ + ⋅ ⋅σ

a

:

49ere T= is t9e torue at t9e 4or@ =ear s9a<t in 7 ⋅mmg B= B4⋅u "+ is

t9e nu@6er o< teet9 o< t9e 4or@ =ear ,it s9oul5 6e roun5e5 o<< to t9e

nearest inte=er nu@eral/g B4

is t9e nu@6er o< t9rea5s o< t9e 4or@ t9at is

3+



5eter@ine5 a88or5in= to ta6le )*%g 4 is t9e 4or@ 5ia@eter <a8tor 49ose

@ini@u@ value is <oun5 as4

@inI #*"$"⋅B= ,o6taine5 @a=nitu5e o< 4

@ust 6e roun5e5 o<< to t9e =reater si5e a88or5in= to t9e <ollo4in=

stan5ar5 series +g $#g $"*.g $%g $)g "#/g E tr is t9e trans<or@e5 @o5uluso< elasti8ity t9at is 5eter@ine5 6y t9e <or@ula

4 =

tr 4 =

" E EE

E E

× ×=

+ *

49ere E4 is t9e 4or@ @aterial @o5ulus o< elasti8ity ,<or steels E

"*$⋅$#. MPa/g E= is t9e 4or@ =ear @aterial @o5ulus o< elasti8ity ,<or

6ronBes an5 8ast irons E … #*⋅$#. MPa/*

Table 0.*Nm0e& #$ th&ea!" #$ the #&m

!elo8ity ratio u + to $% over $% to 3# over 3#

Nu@6er o< t9rea5s B4 % " $

O6taine5 value o< a& s9oul5 6e roun5e5 o<< to t9e =reater si5e

a88or5in= to stan5ar5 series =iven in ta6le )*.*

Table 0./

Stan!a&! 'a*e" #$ the %ent&e !i"tan%e a #$ the #&m gea&ing

Series $ %# .# )3 +# $## $". $)# "## ".# 3$. %## .##

Series " $%# $+# "". "+# 3.. %.#

In our 8ase7 u "#: B4 ": B= "⋅"# %# "+4

@inI #*"$"⋅%# = +*%+ roun5 o<< to t9e

4

@inI $#

. ..

tr . .

" "*$ $# #* $#

$*") $#E "*$ $# #* $#

× × × ×= = ×× + × *

3 .

43 "

$# $-.# $# $*") $##*)". $ $%@@

$#%#"%#

%#

a× × × = × + × = ÷ × ÷

Roun5 o<< t9e o6taine5 value o< a4 to t9e "## @@*

)*.*"* Deter@ine t9e aial @o5ule

3



4

4 =

"@

I B

⋅=

+a

an5 roun5 o<< o6taine5 value a88or5in= to stan5ar5 series =iven in ta6le

)*)*

Table 0.0 Stan!a&! 'a*e" #$ m#!*e m $#& #&m gea&ing

@ :@@ "*.g 3*$.g %g . )*3g +g $#g $"*.

4 +g $#g $"*.g $)g "# +g $#g $"*.g $%g $)g "#

In our 8ase7

" "##@ +@@

$# %#

×= =

+)*.*3* In or5er to ensure stan5ar5 value o< t9e 8entre 5istan8e 4e use

@o5i<ie5 4or@ =ear 4it9 o<<set <a8tor 5eter@ine5 as

4 4 =#*. , B /@

= − ⋅ +a 3

*

To avoi5 un5er8uttin= t9e 8on5ition $ $− ≤ ≤ s9oul5 6e 8arrie5 out*

Ot9er4ise: it is ne8essary to 89an=e a4: 4 or B=*

In our 8ase7

"###*. ,$# %#/ #+ 3 = − × + =

)*.*%* S;e8i<y t9e velo8ity ratio o< t9e 4or@ =earin==

a8t 4

Bu

B=

an5 5eter@ine t9e error

a8tu u

$##mu

−ε = ×

t9at @ust 6e less or eual to %m*

a8t %#u "#"= =

g #mε =)*.*.* Deter@ine t9e ;it89 5ia@eter o< t9e 4or@

54 @⋅4 +⋅$# +# @@*

)*.*)* Deter@ine t9e a55en5u@ 8ir8le 5ia@eter o< t9e 4or@4

a 45 5 " @ +# " + )@@= + × = + × = *

)*.*-* Deter@ine t9e 5e5en5u@ 8ir8le 5ia@eter o< t9e 4or@4 4< 5 5 "*% @ +# "*% + )#*+@@= − × = − × = *

%#



)*.*+* Deter@ine t9e t9rea5e5 len=t9 o< t9e 4or@ 6y @eans o<

ta6le )*-*

Table 0.4 Th&ea!e! *ength #$ the #&m 0

S9i<t <a8tor Nu@6er o< t9rea5s o< t9e 4or@ B4

$g " %

# 64 ≥ ,$$z#*#)⋅B=/q@ 64 ≥ ,$"*.z#*#⋅B=/q@

#*. 64 ≥ ,+z#*#)⋅B=/q@ 64 ≥ ,*.z#*#⋅B=/q@

$*# 64

≥ ,$#*.zB4

/q@ 64

≥ ,$#*.zB4

/q@z#*. 64 ≥ ,$$z#*$⋅B=/q@ 64 ≥ ,$"*.z#*$⋅B=/q@

z$*# 64 ≥ ,$"z#*$⋅B=/q@ 64 ≥ ,$3z#*$⋅B=/q@

7ote. hro@ @anu<a8turin= 8onsi5eration: t9e t9rea5e5 len=t9 o<

9o66e5 an5 =roun5 4or@s is in8rease5 6y ". @@ at @ $# @@: 6y 3.

to %# @@ at @ $# @@ to $) @@ an5 6y .# @@ at @$) @@*

64 ≥ ,$$z#*#)⋅%#/q+ $#-*" @@

Assu@e $#-*" ". $3"

&

b mm= + ≈)*.** Deter@ine t9e lea5 an=le o< t9e 4or@

4

4

B "ar8t= ar8t= $$*3

$#I

γ = = = ÷ ÷

o

)*.*$#* Deter@ine t9e ;it89 5ia@eter o< t9e 4or@ =ear

5= @⋅B= +⋅%# 3"# @@*

)*.*$$* Deter@ine t9e a55en5u@ 8ir8le 5ia@eter o< t9e 4or@ =ear = =a5 5 " @ ,$ / 3"# " + ,$ #/ 33)@@ 3= + × × + = + × × + =

)*.*$"* Deter@ine t9e 5e5en5u@ 8ir8le 5ia@eter o< t9e =ear = =

< 5 5 " @ ,$*" / 3"# " + ,$*" #/ 3##*+@@ 3= − × × − = − × × − =

)*.*$3* Deter@ine t9e @ai@u@ 5ia@eter o< t9e 4or@ =ear

= =

a @a a 4

) @ ) +5 5 33) 3%+@@

B " " "

× ×= + = + =

+ +)*.*$%* Deter@ine t9e <a8e 4i5t9 o< t9e 4or@ =ear

%$



= 4

a 6 #*-. 5≤ × <or B4 $g "

= 4

a 6 #*)- 5≤ × <or B4 %*

= 6 #*-. ) -"@@≤ × =

)*.*$.* Deter@ine t9e ;eri;9eral s;ee5 at t9e 4or@ an5 t9e 4or@ =ear 4 4 3

4 5 n +# $# %%$*-.! $*+.@ Ase8

)# )#

−π× × π× × ×= = =

g

an5= = 3

= 5 n 3"# $# ""*$! #*3-@ se8

)# )#

−π× × π× × ×= = =

)*.*$)* S;e8i<y t9e sli;;a=e s;ee54

sl

! $*+.! $*+@ se8

8os 8os$$*3= = =

γ o

)*.*$-* Deter@ine t9e e<<i8ien8y o< t9e 4or@ =earin=

t=

t= , †/

γ η =

γ + ρ:

49ere ρ† is t9e <ri8tion an=le 5eter@ine5 6y @eans o< ta6le )*+*

Table 0.5Ang*e #$ $&i%ti#n @

Sli;;a=e

s;ee5 !sl: @s

An=le o<

<ri8tion: ρ†

Sli;;a=e

s;ee5 !sl: @s

An=le o<

<ri8tion: ρ†

#*$ %°3#′ .°$#′ "*. $°%#′ "°"#′#*. 3°$#′ 3°%#′ 3 $°3#′ "°$#′$*# "°3#′ 3°$#′ % $°"#′ $°%#′

$*. "°"#′ "°.#′ - $°##′ $°3#′"*# "°##′ "°3#′ $# #°..′ $°"#′

7ote* Greater values o< ρ† 8orres;on5 to tinless 4or@ =ears*

In our 8ase7 ρ† "°$#†g

t=$$$+#*+3%

t= ,$$$+ " $# /

′η = =

′ ′+

o

o o

)*.*$+* Deter@ine <or8es in t9e en=a=e@ent o< t9e 4or@ =earin=

turnin= <or8e at t9e 4or@

4

th

an5 aial <or8e at t9e 4or@ =ear

=

ah

7

%"



4 34 =

t a 4

" T " $#. $#h h ")".N

5 +#

× × ×= = = =

g

aial <or8e at t9e 4or@

4

ah

an5 turnin= <or8e at t9e 4or@ =ear

=

th

7= 34 =

a t =

" T " $-.# $#h h $#3-:.N

5 3"#

× × ×= = = =

g

ra5ial <or8e hr 7=

r t 4h h t= $#3-*. t="# 3+#*N= × α = × ° = *

)*.*$* Deter@ine t9e @ai@u@ 8onta8t stress

( )

= "H tr

H "= 4

4

T K E 8os$*$+

5 5 sin "α

⋅ ⋅ ⋅ γ = ⋅σ

⋅ ⋅ ε ⋅ξ ⋅ δ ⋅ α :

49ere T= is in 78mmg ‡ #*-. is t9e <a8tor 49i89 is use5 to ta>e into

a88ount t9e <a8t t9at 8onta8t o< t9e 4or@ an5 t9e 4or@ =ear o88urs not

alon= t9e 49ole ar8 o< 8onta8t 5e<ine5 6y t9e =ear <a8e an=le "δ , "δ …

$##ˆ $*-. ra5/g ~ is t9e 8onta8t ratio 5eter@ine5 as

( ) "

= = =#*#3 B B $ #*$- B "* "*.α ε = × + + − × + ÷ g

K H K Hβ j K H! is t9e 5esi=n loa5 <a8tor*Table 0.6

(#&m !e$#&mati#n $a%t#&

Nu@6er o<

t9rea5s o< t9e

4or@ B4

kor@ 5e<or@ation <a8tor at o<

+ $# $"*. $% $) "#

$ -" $#+ $.- $-) "". "%+

" .- +) $". $." $-$ $-

3 .$ -) $$# $3% $%+ $-#% %- -# $#$ $"3 $3- $.-

( )

3=

H $

BK $ $ β

= + × − ÷Θ is t9e loa5 8on8entration <a8torg Θ is t9e

4or@ 5e<or@ation <a8tor ,ta6le )*/g $ is use5 to ta>e into a88ount loa5

nature ,<or 8onstant loa5 $#*)/g K H! is t9e 5yna@i8 loa5 <a8tor

5eter@ine5 6y @eans o< ta6le )*$# ,<or 4or@ =earin=s 4e ta>e - or +

a88ura8y o< @anu<a8turin=/*

%3



Table 0.1>D,nami% *#a! $a%t#& 7 H=

De=ree o<

a88ura8y

Dyna@i8 loa5 <a8tor K H! at !sl ,@se8/ o<

u; to $*. $*. 3 3 -*. -*. $"- $*# $*# $*$ $*"

+ $*$. $*". $*%

$*".

O6taine5 value o< wH s9oul5 8orres;on5 to t9e <ollo4in= 8on5ition

wH ,#*+$*$/qwH x*



In our 8ase7( )( )"

#*#3 %# %# $ #*$- %# "* A "*. $:+-)αε = × + + − × + =g

( )3

H

%#K $ $ #:) $:#%

+)β

= + × − = ÷ g K H! $*".g

K H $*#% j $*". $*3-g ‡ #*-.g "δ … $##ˆg

( )

3 . "

H "$-.# $# $*3 $*") $# $$*38os$*$+ "%3*3"MPa$*-.3"# +# $*+-) #*-. sin " "#"

× × × × × °σ = × =× × × × × ×o

w " ,#*+$*$/qw " x,#*+$*$/q"%#$"")% MPa*

Stren=t9 8on5ition is satis<ie5*

)*.*"#* Deter@ine t9e @ai@u@ 6en5in= stress

=

t 6 6 6 6=

n

h K #*- x

6 @

⋅ ⋅= ⋅ ≤ σσ

⋅ :

49ere K 6 is t9e 5esi=n loa5 <a8tor ,K 6 K H/g @n @⋅8osγ is t9e @o5ule

at t9e nor@al se8tiong 6 is t9e toot9 <or@ <a8tor 5eter@ine5 6y @eans

o< ta6le )*$$ 5e;en5in= on t9e nu@6er o< teet9 o< t9e euivalent

strai=9t s;ur =ear =

=

v 3

BB

8os=

γ *

%%



Table 0.11T##th $#&m $a%t#& Y b

+ "+ 3# 3" 3. %# %. .# )# +# $## $.# 3##

b $*+ $*-) $*-$ $*)$ $*.. $*%+ $*%. $*% $*3% $*3 $*"- $*"%

In our 8ase7 @n +⋅8os $$*3# -*+%)g K 6 $*"-g

=

v 3

%#B %":3- %"

8os $$*3= = ⇒

° g

hro@ ta6le )*$$ toot9 <or@ <a8tor 6 $*."g

6 6

$#3-*. $*"- $*."

#*- ")*-"MPa x-" -*+%)

× ×

= × = < σσ ×Stren=t9 8on5ition is satis<ie5*

)*)* Deter@ine t9e te@;erature o< t9e oil 8ontainin= in t9e 8asin=

( )4

oil air oil

t

P $ xt t t

K A

⋅ − η= + ≤

⋅:

49ere tair "#°C is t9e te@;erature o< t9e airg P4 is t9e ;o4er at t9e

4or@ in W g η is t9e e<<i8ien8y o< t9e 4or@ =earin=g K t is t9e 9eattrans<er <a8tor ,<or 8ast iron 8asin=s K t $.$+ k@"⋅C°/g ? is t9e area

o< t9e 8oolin= sur<a8e 5eter@ine5 a;;roi@ately 5e;en5in= u;on t9e

8enter 5istan8e a4 6y @eans o< ta6le )*$"g toilx is t9e allo4a6le

te@;erature o< t9e oil ,<or in5ustrial oils toilx +#.°C/*

Table 0.12C##*ing "&$a%e a&ea A #$ the #&m gea& "+ee! &e!%e&

a4: @@ +# $## $". $%# $)# $+# "## "". ".# "+#A: @" #*$ #*"% #*3) #*%3 #*.% #*)- #*+ $*# $*" $*%

In our 8ase7

3$-.# $*"%*#3 $#

#*+3%

g g & T

P W ω

η

× ×= = = ×

g

Assu@e t9at K t $-g t9e area o< 8oolin= sur<a8e ? #*+ @",ta6le

)*$"/

%.



T9us

( )3

oil oil

%*#3 $# $ #*+3%"# )*$ C xt t

$- #*+

× × −= + = <

×o

*

Con5ition is satis<ie5*

%)



B. ANALSIS O/ THE /LAT )ELT DRI=E

Let us 8arry out t9e analysis o< t9e <lat 6elt 5rive i< in;ut ;o4er

P 1)*) >kg torue at t9e 5rivin= ;ulley T $%" Nj@g velo8ity ratio o< t9e 6elt 5rive ubd "*$.g rotational s;ee5 o< t9e 5rivin= ;ulley n$$... r;@*

-*$* Deter@ine t9e 5ia@eter o< t9e s@aller,5rivin=/ ;ulley

d $≈3 33

$) ) %" $# "#+*) @@T × = × × =

:

49ere T $ is in N⋅@@*

Roun5 o<< t9e 5ia@eter to t9e nearest stan5ar5 value a88or5in= to

t9e <ollo4in= series7 )3: -$: +# #: $##: $$": $".: $%#: $)#: $+#: "##:

""%: ".#: "+#: 3$.: 3..: %##: %.#: .##: .)#: )3#: -$#: +##: ##: $###:$$"#*

Assu@e d $""% @@*

-*"* Deter@ine t9e 5ia@eter o< t9e lar=er ;ulley ta>in= into

a88ount a relative s;ee5 loss #*#$m

d " d $⋅ ubd j,$/""%j"*$.j,$#*###$/%+$*..@@*

an5 roun5 o<< o6taine5 @a=nitu5e a88or5in= to t9e series o< stan5ar5

values*Assu@e d ".## @@*

-*3* S;e8i<y t9e velo8ity ratio o< t9e 6elt 5rive

( ) ( )"

$

.##"*"3"

$ ""% $ #*###$bd

d u

d = = =

× − ε × −*

Error s9oul5 6e ≤ % m*

"*"3" "*$.$##m 3*)m

"*$.

−× =

% m*-*%* Deter@ine t9e 8enter 5istan8e

a = 2⋅@d $ z d "/ "⋅,""% z .##/$%%+@@*

-*.* Co@;ute t9e 8onta8t an=le

" $

$

.## ""%$+# )# $+# )# $)+*.)

$%%+

d d

a

− −= − × = − × =α

*

-*)* Deter@ine t9e 6elt len=t9

%-



( ) "

"" $

$ "

"-)" #*. , / " $%%+ #*. 3*$% -"% %#3"*-@@

% % $%%+

d d # a d d

a

−= × + × π × + + = × + × × + =

× × *

-*-* Deter@ine t9e 6elt s;ee5

$ $ 3*$% #*""% $%..$-*#.) @Ase8

)# )#

d nV π × × × ×= = =

*

-*+* Deter@ine t9e turnin= ,tan=ential/ <or8e

$ )*)3++*#) N

$-*#.)t

P F

V > = =

*

-** C9oose t9e ru66eriBe5 <a6ri8 6elt a88or5in= to ta6le -*$*

In our 8ase 4e ta>e t9e ru66eriBe5 <a6ri8 6elt 0 +## 4it9 t9e nu@6er

o< ;lies + 3 an5 t9i8>ness o< ea89 δ# $*. @@ ,in8lu5in= t9e ru66er interlayers/g t9e @ai@u@ allo4a6le loa5 to t9e ;ly p# 3 N@@ o< 4i5t9*

Table 4.1R00e&i?e! $a0&i% 0e*t" GOST -331;BF

ha6ri8 ;lies

0 +## 0(‰

Š

$.# ("#

No@inal stren=t9 in N ;er @@ o<

4i5t9

.. .. $.# "##

Mai@u@ allo4a6le loa5 ;# to a ;ly in N ;er @@ o< 4i5t9

3 3 $# $3

Desi=n t9i8>ness ‹# o< <a6ri8 ;lies

4it9 ru66er interlayers: @@$*. $*" $*" $*3

Nu@6er o< ;lies i< 6elt 4i5t9 6: @@

"#-$

+#$$"

$"..)#

3.

3)

3)

3.

3)

3)

3%

3%

C9e8> t9e reuire@entδδ#⋅ + ≤ #*#".⋅d $g

$*.j3≤#*#".⋅""%g %*.≤.*)@@* Con5ition is satis<ie5*

-*$#* Deter@ine 8onta8t an=le <a8tor A ~

$$ #*##3 ,$+# / $ #*##3 ,$+# $)+*.)/ #*))A α = − × − α = − × − = *

-*$$* Deter@ine <a8tor A : 49i89 is use5 to ta>e into a88ount t9e

e<<e8t o< t9e 6elt s;ee5

%+



A $*#% #*###% ⋅V "$*#% #*###% ⋅$-*#.)"#:"3)*

-*$"* Deter@ine servi8e <a8tor A s7

A s $ <or stea5y o;eration ,6elt 8onveyers: lat9es an5 =rin5in=

@a89ines/g

A s#* in t9e 8ase o< @o5erate vi6ration ,89ain 8onveyers an5 @illin=

@a89ines/g

A s#*+ in t9e 8ase o< 8onsi5era6le vi6ration ,<li=9t 8onveyers: ;lanin=

@a89ines/*

T9e value o< A s is to 6e re5u8e5 6y #*$ in t4os9i<t o;eration an5

6y #*" in t9rees9i<t o;eration*

Let us assu@e t9at 4e 9ave @o5erate vi6ration* T9at is 49y

A s#**-*$3* Deter@ine <a8tor A Œ: 49i89 is use5 to ta>e into a88ount t9e

6elt ;osition in t9e s;a8e*

A Œ $ <or 9oriBontal 5rives an5 in8line5 at u; to )#°g

A Œ #* <or 5rives in8line5 at over )#° to +#°g

A Œ #*+ <or 5rives in8line5 at over +#° to #°*

In our 8ase 4e assu@e A Œ $*

-*$%* Deter@ine t9e allo4a6le loa5 to $@@ o< ;ly 4i5t9: N@@

px p# ⋅ A α ⋅ A V ⋅ A s ⋅ A Θ3j#*))j#*"3)j#*j$"*%# N@@*

-*$.* hin5 t9e 6elt 4i5t9

3++*#)%3*$"@@

x 3 3

t F b

+ p≥ = =

× ×

an5 roun5 o<< o6taine5 @a=nitu5e a88or5in= to series o< stan5ar5

values7 "#g ".g 3"g %#g .#g )3g -$g +#g #g $##g $$"g $".g $%#g $)#g $+#g

"## an5 so on* Assu@e b.# @@*

-*$)* Deter@ine t9e ;ulley 4i5t9 B a88or5in= to ta6le -*"*

Table 4.2Dete&mining the +**e, i!th B

?elt 4i5t9 b: @@ "# ". 3" %# .# )3 -$ +# # $#

#

$$" $"

.

$%

#

$)#

Pulley 4i5t9 B: @@ ". 3" %# .# )3 -$ +# # $#

#

$$" $"

.

$%

#

$)

#

$+#

In our 8ase 4e assu@e B )3 @@*

-*$-* Deter@ine t9e ;retension in t9e 6elt

%



# # b F = σ × × $*+j.#j%*.%#. N:

49ere σ# $*+ MPa tensile ;restress*

-*$+* Deter@ine tension o< t9e 6elton t9e ti=9t si5e F $ F # z #*.q F t %#.z#*.j3++*#).*#3 N:

on t9e sla8> si5e F " F # #*.q F t %#.#*.j3++*#)"-#*- N

-*$* Cal8ulate t9e <or8e a8tin= on t9e s9a<t an5 6earin=s

$#

$)+*.)3 sin 3 %#. sin $"#+* N*

" "b F F

α= × × = × × =

-*"#* Deter@ine tensile stress

$$

.*#3"*))"MPa

.# %*.

F

b

= = =σ

× δ × *-*"$* Deter@ine 6en5in= stress

$

%*.$## "*##MPa

""%b E

d

δ= × = × =σ

:

49ere E is @o5ulus o< elasti8ity o< t9e 6elt @aterial* hor ru66eriBe5

<a6ri8 6elts E $##÷"## MPa*

-*""* Deter@ine tensile stress 5ue to a8tion o< 8entri<u=al <or8e F c

)" ) " #*3"MPa$# $$## $-*#.) $#c V

−−

= ρ × × = =σ × × :

49ere ρ is 5ensity o< 6elts* hor ru66eri@;re=nate5 <lat 6elts ρ $$## ÷$"## >= @3*

-*"3* Deter@ine t9e @ai@u@ stress

$ xma3 b c= + + ≤ σσ σ σ σ *

hor ru66eriBe5 <a6ri8 6elts wx - MPa*

$ "*))" "*## #*3" %*$MPa x - MPa*ma3 b c= + + = + + = < σ =σ σ σ σCon5ition is satis<ie5*

-*"%* Deter@ine t9e servi8e li<e o< t9e 6elt) -

$# )

$#"### 9ours

" 3)##

i l

ma3

A A "

− × × ×σ= ≥× × × λσ :

49ere σ$ is li@it o< en5uran8e ,<or ru66eriBe5 6elts σ$- MPa/g

$-*#.)%*""

%#3"*-

V

#λ = = =

is t9e nu@6er o< 6elt runs ;er se8on5g

.#



33$*. #*. $*. "*"3" #*. $*%%i bd uA ≈ × − = × − = ta>es into a88ount t9e

velo8ity ratiog A l is use5 to ta>e into a88ount t9e nature o< t9e loa5 ,<or

8onstant loa5 A l $g <or varia6le loa5 A l"/* ke assu@e t9at loa5 is

varia6le*) - ) -

$# ) )

$*%% "$# - $#..)+*" "### 9ours

" 3)## " 3)## %*""%*$

i l

ma3

A A "

− × × × × × ×σ= = = >× × × λ × × ×σ *


.$



. ANALSIS O/ THE CHAIN DRI=E

Let us 8arry out t9e analysis o< t9e 89ain 5rive <or stren=t9 i<

torue at t9e 5rivin= s;ro8>et T $ %)%*. Nj@g torue at t9e 5rivens;ro8>et T " $$#. Nj@g rotational s;ee5 o< t9e 5rivin= s;ro8>et n$

$""*". r;@: rotational s;ee5 o< t9e 5riven s;ro8>et n" %+* r;@;

velo8ity ratio o< t9e 89ain 5rive ucd "*.g in;ut ;o4er o< t9e 89ain 5rive

P $ .*%- >k*

+*$* Deter@ine t9e nu@6er o< teet9 o< t9e 5rivin= s;ro8>et

B$ 3$ "⋅u85 ≥ $-

an5 roun5 o<< o6taine5 @a=nitu5e to t9e nearest inte=er nu@eral*

In our 8ase B$ 3$ "⋅"*. ")Assu@e B$ ") $-*

+*"* Deter@ine t9e nu@6er o< teet9 o< t9e 5riven s;ro8>et

B" B$⋅u85 ≤ $"#

an5 roun5 o<< to t9e nearest inte=er nu@eral

B" ")⋅"*. ).

Assu@e B" ). $"#*

+*3* S;e8i<y t9e velo8ity ratio an5 5eter@ine t9e error "

85

$

B ).u "*.

B ")= = =

*

T9e error s9oul5 6e ≤ % m*

In our 8ase # m*

+*%* Deter@ine t9e servi8e <a8tor K s

K s K ⋅K a⋅K lu6⋅K γ ⋅K 5⋅K ten:

49ere $ is use5 to ta>e into a88ount t9e loa5 nature an5 ta>en as $ in

uiet o;eration an5 as $*" to $*. in t9e 8ase o< s9o8>s an5 i@;a8tsg $ a is

t9e 8enter 5istan8e <a8tor assu@e5 as $ a$ <or a 3#⋅t to .#⋅t an5

$ a#*+ <or a )#⋅t to +#⋅tg $ lub is lu6ri8ation <a8tor , $ lub#*+ <or

i@@ersion lu6ri8ation: $ lub$ <or 5ro;<ee5 lu6ri8ation an5 $ lub$*. <or

;erio5i8 =reasin=/g K γ a88ounts <or t9e an=le t9at t9e s9a<t 8entre line

."



@a>es 4it9 t9e 9oriBontal ,K γ $ <or γ ≤ )#• an5 K γ $*". <or γ )#•/g K 5

is a 5uty <a8tor ,K 5$ <or ones9i<t o;eration: K 5$*". <or t4os9i<t

o;eration an5 K 5$*. <or t9rees9i<t o;eration/g K ten a88ounts <or t9e

@anner o< tension 8ontrol ,K ten$ <or 5rives 4it9 89ain ti=9teners:

K ten$*$. <or 5rives 4it9 a5usta6le 6ases: an5 K ten$*". <or <ie56ase

5rives/*

In our 8ase 4e 9ave s@all s9o8>s an5 i@;a8ts , $ $*"/g t9e 8enter

5istan8e is a = %#⋅t , $ a=$/g ;erio5i8 =reasin= , $ lub=1.//g γ ≤ )#• an5

, $ γ $/g ones9i<t o;eration , $ d $/g <ie5 6ase 5rive , $ ten$*"./*

K s $*"j$j$*.j$j$j$*". "*".

+*.* A;;roi@ately 5eter@ine t9e allo4a6le @ean ;ressure on t9e

9in=es 6y @eans o< ta6le +*$ 5e;en5in= on t9e rotational s;ee5 o< t9e

s@aller s;ro8>et*

In our 8ase <or rotational s;ee5 n$$""*". r;@:[ ] p ≈

" MPa*

Table 5.1

A**#a0*e mean +&e""&e +9 in MPa

n$: r;@

C9ain ;it89: @@

$"*- $.*+-. $*#

.

".*% 3$*-

.

3+*$ %%*%

.

.#*+

.# %) %3 3 3) 3% 3$ " "-

$## 3- 3% 3$ " "- ". "3 ""

"## " "- ". "3 "" $ $+ $-

3## ") "% "" "# $ $- $) $..## "" "# $+ $- $) $% $3 $"

-.# $ $- $) $. $% $3

$### $- $) $% $3 $3

$".# $) $. $3 $"

+*)* Deter@ine t9e 89ain ;it893

$ s 33

$

%)%*. $# "*".T K t "*+ "*+ 3$*""@@

;x ") "B

× × ×≥ × = × =

× × :

.3



49ere T$ is in 7 ⋅mm*

Roun5 o<< t9e ;it89 to t9e nearest stan5ar5 value a88or5in= to t9e

ta6le +*$* In our 8ase assu@e t 3$*-. @@*

+*-* S;e8i<y t9e allo4a6le @ean ;ressure a88or5in= to ta6le +*$ 6y

inter;olation ;x* On @ulti;lyin= it 6y

K ; $ z #*#$q,B$$-/ $ z #*#$q,")$-/$*# 4e =et <inite

@a=nitu5e o< ;x "j$*#3$*)$MPa

+*+* Deter@ine t9e e<<e8tive @ean ;ressure*

hor t9at 4e

<in5 89ain s;ee5

$ $

3 3

B t n ") 3$*-. $""*".! $*)+@ se8

)# $# )# $#

× × × ×= = =

× × g

<in5 turnin= ,tan=ential/ <or8e3

$t

P .*%- $#h 3.3*N

! $*)+

×= = =

g

loo> u; t9e ;roe8te5 9in=e area S9 usin= ta6le +*"* In our 8ase

S9")" @@"

T9en t9e e<<e8tive @ean ;ressuret s

9

h K ; ;x

S

×= ≤

*

I< t9is ineuality is not ri=9t it is ne8essary to in8rease t9e ;it89 t*

3.3* "*". ; 3#*%MPa ;x

")"

×= = <*

In our 8ase t9e ineuality is ri=9t*

+** Deter@ine t9e nu@6er o< lin>s in t9e 89ain"

t t

t

" a #*. BLa

Σ∆= × + × +

:

.%



49eret

LL

t=

is t9e 89ain len=t9 in ;it89esgt

aa

t=

g a ≈ ,3#.#/qt g BΣ

B$ z B" g

" $B B

"

−

∆ = × π * Roun5 o<< o6taine5 @a=nitu5e to even inte=er

nu@eral*

In our 8ase7 at %.g BΣ ") z ). $g

)" "))*"$

"

−∆ = =

× π g"

t

)*"$" %. #*. $ $3)*3) $3)L

%.= × + × + = ⇒

+*$#* S;e8i<y t9e 8entre 5istan8e"

"

t t

""

a #*". t ,L #*. B + /L #*. B

#*". 3$*-. ,$3) #*. $ + )*"$ / $%"3*#3@@$3) #*. $

, /

, /

Σ Σ= × × − × + − × ∆ =×

= × × − × + − × =− ×

−

T9e sla8> si5e o< t9e 89ain s9oul5 9ave a sli=9t sa= < ≈ #*#$qa: <or

49i89 ;ur;ose t9e 5esi=n 8entre 5istan8e is re5u8e5 6y #*" to #*% m*

Assu@e t9at a $%$+*-) @@*

+*$$* Deter@ine t9e ;it89 5ia@eters

o< t9e 5rivin= s;ro8>et

;$

$

t 3$*-.")3*%$@@5

$+#$+#sinsin

")B

= = =

÷ ÷

o

g

o< t9e 5riven s;ro8>et

;"

"

t 3$*-.).-*$-@@5

$+#$+#sinsin

).B

= = =

÷ ÷

o

*

+*$"* Deter@ine t9e a55en5u@ 5ia@eters

..



$e $

$

$+#t ,8t= #*-/ #*3$ 5D

B

$+#

3$*-. ,8t= #*-/ #*3$ $*#. "--*+$@@")

= × + − × = ÷

= × + − × = ÷

"e $

"

$+#t ,8t= #*-/ #*3$ 5D

B

$+#3$*-. ,8t= #*-/ #*3$ $*#. )-"*--@@

).

= × + − × = ÷ = × + − × = ÷

49ere 5$ is t9e roller 5ia@eter ,ta6le +*"/*

+*$3* Deter@ine t9e 5e5en5u@ 5ia@eter

$ $ $$ ; ;i , #*$-. / ")3*%$ ,$*#. #*$-. ")3*%$/ "%$*."@@5 5 5D = − + × = − + × =

:

" " "$ ; ;i , #*$-. / ).-*$- ,$*#. #*$-. ).-*$- / )33*)3@@5 5 5D = − + × = − + × =*

+*$%* Deter@ine t9e 4e6 t9i8>ness o< s;ro8>et

C #*3j? 6us9 #*3j$*#. $-*-"@@

49ere ? 6us9 is 5eter@ine5 a88or5in= to ta6le +*"*

.)



Table 5.2Lea!ing +a&ti%*a&" #$ S#'iet;ma!e &#**e& %hain" PR GOST 13<>;B<F

Pit89 t Bbush:

@@

Pin

5ia@eter

5

Roller

5ia@eter

5$

9:

@a

6:

@a

?rea>in=

loa5 h 6r :

>N

Mass ;er

@eter run

: >=

Proe8te

5 9in=e

area S9:

@@"

*.". .*-" 3*"+ )*3. +*. $- *$ #*%. "+*$

$"*- -*-. %*%. +*.$ $$*+ "$ $+*" #*-. 3*)

$.*+-. *). .*#+ $#*$) $%*+ "% ""*- $*# .%*+

$*#. $"*- .*) $$*$ $+*" 33 3$*+ $* $#.*+

".*% $.*++ -*. $.*++ "%*" 3 )#*# "*) $-*-

3$*-. $*#. *.. $*#. 3#*" %) ++*. 3*+ ")"

3+*$ ".*% $$*$" ""*"3 3)*" .+ $"-*# .*. 3%

%%*%. ".*% $"*-" ".*% %"*% )" $-"*% -*. %-3

.#*+ 3$*-. $%*" "+*.+ %+*3 -" "")*+ *- )%)

+*$.* Deter@ine <or8es a8tin= to t9e lin>s

turnin= <or8e

3$

tP .*%- $#h 3.3*++N! $*)+

×= = =g

8entri<u=al <or8e h8 ⋅!" 3*+ ⋅ $*)+" $#*-3 N: 49ere is t9e

@ass ;er @eter run o< t9e 89ain in kg ,ta6le +*"/g

loa5 5ue to 89ain 5e<le8tion h< *+$⋅ K < ⋅⋅⋅a: 49ere K < $ <or

verti8al 8entre line arran=e@ents: K < ) <or 9oriBontal 8entre line

arran=e@ents an5 K < $*. <or t9e 8entre line arran=e@ent on t9e an=le

%.o*

In our 8ase 8entre line is arran=e5 on t9e an=le %.o: t9us K < $*.

.-



h< *+$⋅ $*. ⋅ 3*+ ⋅ $*%"3 -*.- N*

+*$)* Deter@ine t9e 5esi=n loa5 on t9e s9a<t

hs9a<t ht z "jh< 3.3*++ z " j -*.- 3)*#" N*

+*$-* Deter@ine t9e sa<ety <a8tor

6r

t 8 <

hS Sx

h K h h= ≥

× + +:

49ere h 6r is t9e 6rea>in= loa5 in N, ta6le +*"/g K is t9e 5yna@i8 <a8tor

ta>in= into a88ount t9e loa5 nature ,;*+*%/g Sx is stan5ar5 sa<ety <a8tor

,ta6le +*3/*

Table 5.)

Stan!a&! $a%t#&" #$ "a$et, S $#& PR R#**e& %hain"

n$: r;@C9ain ;it89 t: @@

$"*- $.*+-. $*#. ".*% 3$*-. 3+*$ %%*%. .#*+

.# -*$ -*" -*" -*3 -*% -*. -*) -*)

$## -*3 -*% -*. -*) -*+ +*# +*$ +*3

3## -* +*" +*% +* *% *+ $#*3 $#*+

.## +*. +* *% $#*" $$*# $$*+ $"*.

-.# *3 $#*# $#*- $"*# $3*# $%*#

$### $#*# $#*+ $$*- $3*3 $.*# $".# $#*) $$*) $"*- $%*.

In our 8ase7

h 6r ++*. >N: K $*": Sx -*3++*. $#

S "#*% Sx3.3*++ $*" $#*-3 -*.-

×= = >

× + + *


.+



. ANALSIS O/ SHA/TS

Let us 5esi=n t9e s9a<ts 8onstru8tion an5 8arry out stren=t9 analysis

o< t9e out;ut s9a<t i< torue at t9e out;ut s9a<t T is eual to %## Nj@**$ Deter@ine t9e @ini@u@ 5ia@eter o< s;ee5 re5u8er s9a<ts

3

#*" xmin

T d =

× τ:

49ere T is t9e torue at t9e s9a<t in Nj@@g x is t9e allo4a6letan=ential stress 5ue to torsion in MPa*

In or5er to 8o@;ensate a8tion o< 6en5in= stresses t9e allo4a6letan=ential stress 5ue to torsion is assu@e5 as 5o4n rate5* hor steels

x$."# MPa*O6taine5 @a=nitu5e o< d min is roun5e5 o<< to t9e =reater si5ea88or5in= to t9e <ollo4in= stan5ar5 series7 "#: "$: "": "3: "%: ".: "):"+: 3#: 3": 3%: 3): 3+: %#: %": %.: %+: .#: .": ..: .+: )#: ).: -#: -.: +#:+.: #: .: $##:$#.: $$#: $$.: $"#: $3#: $%#: $.#*

I< t9e s;ee5 re5u8er s9a<t is oine5 4it9 t9e ele8tri8al @otor s9a<tt9e <ollo4in= 8on5ition s9oul5 6e 8arrie5 out

d moto d min $# @@:49ere d moto is t9e 5ia@eter o< t9e ele8tri8al @otor s9a<t ,ta6le *$/*

*"* Desi=n t9e 8onstru8tion o< s;ee5 re5u8er s9a<ts*

In =eneral ;ur;ose s;ee5 re5u8ers ste;;e5 s9a<ts 4it9 soli5 8ross

se8tion are use5 as a rule*

hor t9e in;ut s9a<t d min is t9e 5ia@eter o< t9e s9a<t 8antilever

;ortion 49ere su89 ele@ents as a 9al< 8ou;lin=: a ;ulley: a s;ro8>et or a

;inion @ay 6e @ounte5 ,hi=**$/* In or5er to <i a6ove @entione5

ele@ents in t9e aial 5ire8tion 4e use a s9oul5er 49i89 9ei=9t t$ @ay 6e

ran=e5 <ro@ " to . @@ 5e;en5in= on t9e s9a<t 5ia@eter* Re8o@@en5e5

values o< t$ are =iven in ta6le *"*T9e net s9a<t ;ortion o< 5ia@eter d "d $z"jt $ ,t9e value o< d " @ust

8orres;on5 to stan5ar5 series/ is <or installin= a seal* Seals are use5 to

;revent 6earin= asse@6lies <ro@ <in5in= 5ust an5 5irt an5 to re@ain

lu6ri8ation o< 6earin=s* hor =eneral ;ur;ose s;ee5 re5u8er li; seals are

use5 @ore <reuently*

In or5er to re5u8e <ri8tion at t9e ;oint o< 8onta8t o< t9e seal 4it9

t9e s9a<t 8orres;on5in= ;ortion s9oul5 6e ;olis9e5* hor t9is ;ur;ose t9is

;ortion is a55itionally sur<a8e 9ar5ene5 to 9ar5ness %..# HRC*

.



Table 6.1O'e&a** an! m#nting !imen"i#n" #$ "e&ie" 5A th&ee;+ha"e in!%ti#n

m#t#&" GOST 1<-3;1F

Ty;e5esi=na

tion

Nu@6er o<

;oles

Overall5i@ensions

Mountin= 5i@ensions

# " D d h$ l $ l " l 3 b d $

%A#L

"g%g)g+

3.# "%3 "#+ "% # .# .)$"

.

$%

#$#

%A$##S 3). ").

"3. "+$#

#)# )3

$3

" $)

#$"

%A$##L 3. "+#$%

#

%A$$"M %." 3$# ")# 3" $$" +# -#$%

#

$

#$"

%A$3"S %+#3.# 3#" 3+

$3

"+# +

$-

+

"$

)$"

%A$3"M .3#

%A$)#S"

)"%

%3# 3.+

%"

$)

#$$#

$"

$

$-+ ".

%$.

%g)g+ %+

%A$)#M"

))-%" "$

#%g)g+ %+

d

1

l

d

l 1 l 2 l ) b

h 1

"

D

)#



hi=**$* In;ut s9a<t

Table 6.2Re%#mmen!e! 'a*e" #$ t 1 an! t -

d : @@ "# .# .. $"#

t $: @@ "g "*. .

t ": @@ $g $*. "*.

T9e net ;ortion o< t9e s9a<t is <or @ountin= a 6earin=* T9e

5ia@eter o< t9is ;ortion is 5eter@ine5 as

d 3 d " z "jt ":

49ere t " is t9e 9ei=9t o< t9e s9oul5er t9at is use5 <or 5i<<erentiation o<

s9a<t sur<a8es 6y 9ar5ness an5 rou=9ness* Re8o@@en5e5 values o< t "are =iven in ta6le *"* It is ne8essary to note t9at t " s9oul5 6e 89osen to

o6tain s9a<t 5ia@eter 53 en5e5 6y # or .* It is e;laine5 6y t9e <a8t t9at

6earin=s are stan5ar5 ele@ents 4it9 t9e inner rin= 5ia@eter en5e5 6y #

or .*

?earin=s @ust 6e <ie5 in t9e aial 5ire8tion* T9at is 49y t9e

5ia@eter o< t9e net ;ortion o< t9e s9a<t: 49ere a ;inion or =ear isinstalle5: is 5eter@ine5 as

d % d 3 z "jt $*

O6taine5 value o< 5% s9oul5 8orres;on5 to stan5ar5 series*

A ;inion @ay 6e @a5e eit9er as soli5 4it9 t9e s9a<t or as an

in5ivi5ual ;art* In or5er to in8rease s9a<t stren=t9 an5 ri=i5ity it is

re8o@@en5e5 to use ;inion s9a<ts*

T9e last ;ortion o< t9e s9a<t is <or installin= t9e se8on5 6earin=*

T9e 5ia@eter o< t9is ;ortion s9oul5 6e t9e sa@e as <or t9e <irst 6earin=*In our 8ase it is d 3*

T9e out;ut s9a<t 9as t9e sa@e 5esi=n as t9e in;ut one* ?ut in

8ontrast to t9e latter a =ear is @ounte5 on t9e s9a<t ;ortion o< 5ia@eter

d % ,hi=**"/* In or5er to <i t9e =ear in t9e aial 5ire8tion 4e s9oul5

;rovi5e <or t9e s9oul5er o< 9ei=9t t $* T9at is 49y t9e 5ia@eter o< t9e

net ;ortion o< t9e s9a<t is d . d % z "jt $*

hor our 8ase 4e s9oul5 5esi=n t9e out;ut s9a<t 49ere a 9eli8al

s;ur =ear is @ounte5* ke 4ill 9ave t9e <ollo4in= 5ia@eters7

)$



3

3%## $#%)*% @@

#*" "#x

×= =

×mind

*

hi=**"* Out;ut s9a<t

Let us assu@e d min = d $ .# @@ ,a88or5in= to t9e stan5ar5 series/g

d " d $ z "jt $ .# z "j "*. .. @@g

d 3 d " z "jt " .. z "j $*. .+ @@ ,s9oul5 6e 89osen to o6tain

s9a<t 5ia@eter 53 en5e5 6y # or ./g

d % d 3 z "jt $ )# z "j . -# @@gd . 5% z "jt $ -# z "j. +# @@*

hor 6evel ;inion s9a<ts ,hi=**3/ an5 4or@ s9a<ts ,hi=**%/ 4e

s9oul5 intro5u8e t9e a55itional ;ortion o< 5ia@eter d "† 6et4een ;ortions

o< 5ia@eters 5" an5 53* T9is ;ortion is ne8essary to install a slotte5 nut

<or a5ustin= 8learan8es in t9e 6earin=* Dia@eter d "† s9oul5 6e 89osen

a88or5in= to ta6le $"*$*

)"



hi=**3* ?evel ;inion s9a<t

hi=**%* kor@ s9a<t

*3* Deter@ine siBes o< ele@ents t9at are @ounte5 on t9e s9a<t*

*3*$* Pinion*

ha8e 4i5t9 o< t9e ;inion b p = b g z .*

*3*"* S;ur an5 6evel =ears ,hi=**.: a% b/

t9i8>ness o< t9e ri@ ‹ ,3%/qmg

t9i8>ness o< t9e 4e6 A ,#*"#*3/qb g g

5ia@eter o< t9e 9u6 d hub,$*.$*-/qd sha-t g

len=t9 o< t9e 9u6 l hub,$*"$*./qd sha-t g

5ia@eter o< t9e 9ole

#

%

hubhole

D . d d =

g

5ia@eter o< t9e 9ole 8entre line

# hubc

D (d D =

2 g

<illet ra5ii ) @@ an5 an=le Ž - *̂

)3



a b c hi=**.* S;ur =ear ,a/: 6evel =ear ,b/: 4or@ =ear ,c/

*3*3* kor@ =ear ,hi= *.: c/*

t9i8>ness o< t9e 6ronBe rin= ‹$ "qmg

t9i8>ness o< t9e steel ri@ ‹" "qmg

t9i8>ness o< t9e 4e6 A ,#*"#*3/qb g g

5ia@eter o< t9e 9u6 d hub,$*.$*-/qd sha-t g

len=t9 o< t9e 9u6 l hub,$*"$*./qd sha-t g

5ia@eter o< t9e s8re4 d s,$*"$*%/qmg len=t9 o< t9e s8re4 l s,#*3#*%/qb g g

5ia@eter o< t9e 9ole

#

%

hubhole

D d d

−=

g

5ia@eter o< t9e 9ole 8entre line

#

"

hubc

D ( d D =

g

4i5t9 an5 9ei=9t o< t9e 8ollar h #*$.qb g g t #*+qh

<illet ra5ii ) @@ an5 an=le Ž -ˆ*

*3*%* ?earin=s*

T9e ty;e o< a 6earin= 5e;en5s on t9e loa5 it 8an 4it9stan5*

S9a<ts 49ere "t&aight "+& gea&" are lo8ate5 s9oul5 6e installe5

in 6earin=s t9at 4it9stan5 ra5ial loa5 only* hor t9is ;ur;ose 4e use

ra5ial 6all 6earin=s o< li=9t4ei=9t series ,ta6le *3/*

S9a<ts o< he*i%a* "+& gea&" s9oul5 6e @ounte5 on an=ular

8onta8t 6all 6earin=s o< li=9t4ei=9t series ,ta6le *%/ 6e8ause t9ey 8an

;er8eive 6ot9 ra5ial an5 aial loa5s* S9a<ts o< 0e'e* gea&" an5 a #&m

l 9u6 d

s 9 a < t

D c

Ž

d 9 o l e

A

D #

D c

d a m a 3

d s 9 a < t l 9u6

Ž

A

‹ " ‹ $

d 9 o l e

t

hl s

d 9 u 6

d s

d 9 u 6

D #

‹

#*.

Ž

A

‹

l 9u6 d

s 9 a < t

D #

d 9 o l e

D c

d 9 u 6

d a

)%



gea& are @ounte5 on ta;ere5 roller 6earin=s o< li=9t4ei=9t series ,ta6le

*./* It is e;laine5 6y t9e <a8t t9at t9ey 8an 4it9stan5 9eavy aial

loa5s*

(#&m s9a<ts are installe5 in t4o ta;ere5 roller 6earin=s ,ta6le*./ an5 one ra5ial 6all 6earin= o< li=9t4ei=9t series ,ta6le *3/*

Table 6.)Sing*e ; R# Ra!ia* )a** )ea&ing" GOST 33;B<F. Lighteight "e&ie"

d c #*.j, D(d /

D& #*3"j, Dd /! #*$.j, Dd /

Ty;e5esi=nation

d D B ?asi8 loa5ratin= A : >N

Stati8 loa5ratin= A #: >N

"#% "# %- $% $*. $"*- )*"

"#. ". ." $. $*. $%*# )*.

"#) 3# )" $) $*. $*. $#*#

"#- 3. -" $- " ".*. $3*-

"#+ %# +# $+ " 3"*# $-*+

"# %. +. $ " 33*" $+*)

"$# .# # "# " 3.*$ $*+

"$$ .. $## "$ "*. %3*) ".*#

"$" )# $$# "" "*. ."*# 3$*#

"$3 ). $"# "3 "*. .)*# 3%*#

"$% -# $". "% "*. )$*+ 3-*.

"$. -. $3# ". "*. ))*3 %$*#

"$) +# $%# ") 3 -#*" %.*#

"$- +. $.# "+ 3 +3*" .3*#

"$+ # $)# 3# 3 .*) )"*#

"$ . $-# 3" 3*. $#+*# )*.

""# $## $+# 3% 3*. $"%*# -*#

Table 6.*Sing*e;&# ang*a&;%#nta%t 0a** 0ea&ing GOST 31;B<F. Lighteight

na&&# "e&ie" 1-° $#& 3> an! ->° $#& 5>F

Ty;e

5esi=nation

d D B T $ Loa5 ratin=: >N

A A #

).



# * . S

#*$.?

d c #*.j, D(d / D& #*3"j, Dd /! #*$.j, Dd /

3)"#% "# %- $% $% $*. #*. $.*- +*3$

3)"#. ". ." $. $. $*. #*. $)*- *$#

3)"#) 3# )" $) $) $*. #*. ""*# $"*#

3)"#- 3. -" $- $- " $ 3#*+ $-*+

3)"#+ %# +# $+ $+ " $ 3+* "3*"3)"# %. +. $ $ " $ %$*" ".*$

3)"$# .# # "# "# " $ %3*" "-*#

3)"$$ .. $## "$ "$ "*. $*" .+*% 3%*"

3)"$" )# $$# "" "" "*. $*" )$*. 3*3

%)"$3 ). $"# "3 "3 "*. $*" )*% %)*+

3)"$% -# $". "% "% "*. $*" +#*" .%*+

%)"$. -. $3# ". ". "*. $*" -+*% .3*+

3)"$) +# $%# ") ") 3 $*. 3*) ).*#

3)"$- +. $.# "+ "+ 3 $*. $#$*# -#*+

3)"$+ # $)# 3# 3# 3 $*. $$+*# +3*#3)"$ . $-# 3" 3" 3*. " $3%*# .*#

3)""# $## $+# 3% 3% 3*. " $"% $$+

3)""" $$# "## 3+ 3+ 3*. " $%) $3-

Table 6./Sing*e;&# ta+e&e!;&#**e& 0ea&ing" GOST 333;BF. Lighteight "e&ie"9

1-÷1°

d c #*.j, D(d /

d p #*".j, Dd /l p #*)+j B

Ty;e

5esi=

nation

d D T B A d $ d " D$

Loa5 ratin=: >NeA A #

-"#" $. 3. $$*-. $$ ". "# "- $#. )*$ #*%.

-"#3 $- %# $3*". $" $$ "- "" 3" $%*# *# #*3$

-"#% "# %- $.*". $% $" 3" ") 3+ "$*# $3*# #*3)

-"#. ". ." $)*". $. $3 3- 3$ %3 "%*# $-*. #*3)

-"#) 3# )" $-*". $) $% %. 3+ ." 3$*. ""*# #*3)

-"#- 3. -" $+*". $- $. ." %% )# 3+*. ")*# #*3-

-"#+ %# +# $*". $ $) .+ .# )- %)*. 3"*. #*3+

-"# %. +. "#*-. "# $) )3 .. -" .#*# 33*# #*%$

-"$# .# # "$*-. "$ $- )- .+ -+ .)*# %#*# #*3--"$$ .. $## ""*-. "$ $+ -. ). +. ).*# %)*# #*%$

-"$" )# $$# "3*-. "3 $ +" -" . -+*# .+*# #*3.

-"$% -# $". ".*". ") "$ . +3 $#+ )*# +"*# #*3-

-"$. -. $3# "-*". ") "" $## ++ $$3 $#-*# +%*# #*3

-"$) +# $%# "+*". ") "" $$# - $"$ $$"*# .*" #*%"

-"$- +. $.# 3#*.# "+ "% $$3 $## $" $3#*# $#*# #*%3

-"$+ # $)# 3"*.# 3$ ") $"$ $#- $3+ $.+*# $".*# #*3+

-"$ . $-# 3%*.# 3" "- $" $$% $%. $)+*# $3$*# #*%$

-""# $## $+# 3-*## 3% " $3- $"" $.% $+.*# $%)*# #*%$

))



*3*.* Li; seal*

Di@ensions o< li; seals are =iven in ta6le *)*

Table 6.0

Stan!a&! *i+ "ea*" GOST B<-;BFd D h$ d D h$

"#g"$g"" %#

$#

..g.)g.+

+#

$"

"% %$ )# +.

". %" )3g). #

") %. -#g-$ .

3#g3" ." -. $##

3.g3)g3+ .+ +# $#.

%# )# +. $$#

%" )" #g. $"#%. ). $## $".

%+g.# -# $#. $3#

." -. $$# $3.

*3*)* S;ro8>et ,hi= *)/

5ia@eter o< t9e 9u6 d 9u6=,$*.$*-/qd s9a<tg

len=t9 o< t9e 9u6 l 9u6,$*"$*./qd s9a<tg t9i8>ness o< t9e 4e6 A #*3q B 6us9:

49ere ? 6us9 is t9e 6us9 4i5t9 ,ta6le +*"/*

*3*-* Pulley ,hi=* *-/

5ia@eter o< t9e 9u6 d 9u6,$*+"*"/qd s9a<tg

len=t9 o< t9e 9u6 l 9u6,$*."*"/qd s9a<t B: 49ere B is t9e ;ulley 4i5t9g

t9i8>ness o< t9e ri@ ‹#*##.qd z3 @@ghi=**)*S;ro8>et

)-



hi=* N*+* Pulley

d

A

d s 9 a < t

D >

l 9u6

B

d 9 u 6

t9i8>ness o< t9e 4e6 A ,$*#$*"/ q‹

,<or ;ulleys o< 5 3## @@/g

nu@6er o< ar@s + ,<or ;ulleys o< d 3## @@/i< 3## d .## @@ t9an + %

i< d .## @@ t9an + )

5esi=n t9i8>ness o< t9e ar@

[ ]t

33+

b

F d h =

+9

:

49ere Ft is turnin= <or8e o6taine5 in ;*-*+g d is 5ia@eter o< t9e ;ulleyg +

is nu@6er o< ar@sg 9bx is allo4a6le 6en5in= stress ,<or 8ast irons

9bx3# MPa/

*3*+* Cou;lin=*

In @e89ani8al 5rives 4it9 sin=le sta=e s;ee5 re5u8ers 4e use a

8ou;lin= 4it9 ru66er6us9e5 stu5s* Di@ensions o< t9is 8ou;lin= are

=iven in ta6le *-*

hi=**-*Pulley

)+



Table 6.4 Stan!a&! %#+*ing" ith &00e& 0"he! "t!" GOST -15-5 K 3F

TorueT : Nj@ d

D:

not@ore

# l

D$ l $ l " d " d 3 B B$ 5$

Nu@6e

r o< stu5s

Mo5i<i8ation$ " $ "

3$*.$)

# +$ )# %# "+ )3

$) "#

3#

"# %"

+

M+ %$+ 3"

)3*#"#

$## $#% -) .# 3) -$ 3)""

$".

".

$"# $". + )# %" #%#

M$

#)

"+

3# .#

".#

3"

$%# $). $"$ +# .+$#

.

$+ 3"

.)

"+ .%"

3. .)

3) )3

3+ -$

%# -$

%" -.

%. +#

.##

%#

$-# "". $)# $$# +"$3#

-$

M$"

+%" -.

%. +#

$###

%+

""# "") $-# $%#$#

.

$-

#"% %#

+#

3) ).

)

$#

.# #

.. #

)# $##

"###

)3

".#

"++ "$+ $%#$#

.

$-

#

3# %+

$3#

%+ +-

#

M$

)

).

-#

-.

+#

3%+ ")+ $-#$3

#

$

#

$.#+.

#

)



S7ETCH LAOUT

A<ter 5esi=nin= a s9a<t 8onstru8tion an5 5eter@ination o< siBes o<

all ele@ents @ounte5 on a s9a<t it is ne8essary to <in5 5istan8es 6et4een

ele@ents 49i89 are lo8ate5 on a s9a<t* hor t9is ;ur;ose a s>et89 layouto< a s;ee5 re5u8er s9oul5 6e @a5e* In t9is 8ase a s;ee5 re5u8er is 5ra4n

in one ;roe8tion ,to; or <ront vie4/ to s8ale $7$ on ;ro<ile ;a;er*

Let us 8onsi5er as an ea@;le o< ;lottin= a s>et89 layout o< sin=lesta=e s;ur =ear s;ee5 re5u8er*

$* Plot a s;ur =ears ta>in= into a88ount 5i@ensions 49i89 4ere 5eter@ine55urin= stren=t9 analysis an5 in ;**3*$ an5 *3*"* ke 4ill 6e=in <ro@

;lottin= t9e 8entre 5istan8e: ;it89 8ir8le 5ia@eters: a55en5u@ an55e5en5u@ 8ir8le 5ia@eters o< a ;inion an5 a =ear* T9e en=a=e@ent o<

=ears 9as to 6e re;resente5 as in hi=* *+*"* Deter@ine 5is;osition o< inner 4alls o< a s;ee5 re5u8er* In or5er to

eli@inate 8onta8t o< =ears 4it9 a 4all it is re8o@@en5e5 to lo8ate t9einner 4all 6y 5istan8e $# @@ 4it9 res;e8t to a =ear 9u6 an5 6y 5istan8e"# @@ 4it9 res;e8t to =ear <a8e en5*

3* Deter@ine 5is;osition o< 6earin=s* In t9is 8ase 4e s9oul5 ta>e into a88ountt9at inner sur<a8e o< a 6earin= asse@6ly 9as to 6e ;rote8te5 <ro@ =rease4as9in= out* hor t9is ;ur;ose =rease retainin= rin=s are use5 ,hi=*$"*$"/*T9e 4i5t9 o< t9ese rin=s is ran=e5 <ro@ $# to $" @@* T9at is 49y 6earin=sare lo8ate5 6y 5istan8e $# @@ 4it9 res;e8t to s;ee5 re5u8er inner 4all*

%* Plot 6earin=s <or in;ut an5 out;ut s9a<ts usin= 5i@ensions <ro@ ta6les*3*.*

.* Deter@ine 5is;osition o< outer 4alls o< a s;ee5 re5u8er* Outer 4all islo8ate5 6y 5istan8e #*.j?@a: 49ere ?@a is t9e 4i5t9 o< t9e lar=est

6earin=*)* In a s;ee5 re5u8er 6earin= asse@6lies 9ave to 6e ;rote8te5 6y 6earin=

8a;s <ro@ t9e si5e o< s;ee5 re5u8er outer 4alls* T9e 4i5t9 o< t9ese 8a;s

is ran=e5 <ro@ + to $" @@* Let us 5ra4 strai=9t lines 6y 5istan8e $# @@4it9 res;e8t to s;ee5 re5u8er outer 4alls to 5eter@ine a;;roi@ate5is;osition o< 6earin= 8a;s*

-* Plot li; seals <or in;ut an5 out;ut s9a<ts usin= 5i@ensions <ro@ ta6le*)* A seal is lo8ate5 in a 6earin= 8a; 6y 5istan8e 3% @@ 4it9 res;e8tto 6earin= 8a; <a8e en5*

+* Ma>e an ar8 alon= in;ut an5 out;ut s9a<t aes 6y 5istan8e "# @@ 4it9res;e8t to 6earin= 8a;s to 5eter@ine 5is;osition o< t9e <irst s9oul5er o< as9a<t*

-#



* Lay out len=t9 o< an ele@ent @ounte5 on t9e 8antilever ;ortion o< t9es9a<t alon= in;ut an5 out;ut s9a<t aes* In t9is 8ase 4e o6tain etre@e

;oints o< t9e in;ut an5 out;ut s9a<ts*

$#* Dra4 s;ee5 re5u8er s9a<ts ta>in= into a88ount t9eir 8onstru8tion an55ia@eters o< 8orres;on5in= ;ortionsEa@;les o< s>et89 layout o< sin=le sta=e s;ee5 re5u8ers are s9o4n

in hi=* *+*$#*

hi=* *+* S>et89 layout o< sin=le sta=e s;ur =ear s;ee5 re5u8er

-$



hi=* ** S>et89 layout o< 6evel =ears

-"



hi=* *$#* S>et89 layout o< sin=le sta=e 4or@ =ear s;ee5 re5u8er

-3



1. SHA/T ANALSIS /OR STRENGTH

Let us 8arry out t9e analysis o< t9e s9a<t <or stren=t9 i< t orue at t9e

=ear s9a<t T g is eual to 3-# Nj@ an5 <ro@ t9e ;revious analysis 4e9ave t9at turnin= ,tan=ential/ <or8e F t "%)- Ng F ++ Ng F a 3%)*-

Ng d g 3## @@g d -# @@ ,t9e s9a<t ;ortion 5ia@eter 49ere t9e =ear

is @ounte5/: an5 <ro@ t9e s>et89 layout a )3 @@g b )3 @@g c $)%

@@*

$#*$* Sele8t t9e @aterial o< t9e s9a<t*

T9e @ain @aterial o< s9a<ts is @e5iu@8ar6on or alloy steels o<

=ra5e Steel %# ,#*%C/: Steel %. ,#*%.C/: Steel %#p ,#*%CCr/ an5 ot9ers

4it9 9ar5ness H "## ?HN*

Me89ani8al 89ara8teristi8s o< steels are =iven in ta6le $#*$*

Table 1>.1Me%hani%a* Cha&a%te&i"ti%" #$ )a"i% Sha$t Mate&ia*"

Steel =ra5e

?lan>

5ia@eter:

@@,@a

/

?rinell 9ar5ness:

σul σ C

Heat treat@ent

MPa

Steel %. ,#*%.C/ $)# $-# to "$- ?HN )## 3%# Nor@aliBin=

Steel %. ,#*%.C/ "## $" to "%# ?HN -.# %.# Marte@;erin=

Steel %#p

,#*%#CCr/"## "3# to ")# ?HN +.# ..# Marte@;erin=

Steel %#p

,#*%#CCr/$"# ")# to "+# ?HN .# -## Marte@;erin=

Steel %#pH

,#*%#CCrNi/"## "3# to 3## ?HN +.# )## Marte@;erin=

Steel 3.pM

,#*3.CCrMo/ "## "%# ?HN ## +## Marte@;erin=

Steel %#pHM

,#*%#CCrNiMo/$)# 3#" ?HN

$$#

### Marte@;erin=

hor ea@;le: let us 89oose Steel %#p ,#*%CCr/ 9eat treate5 6y

@arte@;erin= to 9ar5ness ran=e5 <ro@ "3# to ")# ?HN: σul +.# MPa:

σ C ..# MPa*

$#*"* Analyse a s9a<t <or stati8 stren=t9*

$#*"*$* Plot t9e analyti8al @o5el o< a s9a<t an5 a;;ly all a8tin=

-%



<or8es ,hi=* $#*$/* In t9is 8ase a s9a<t is 8onsi5ere5 as a 6ea@ @ounte5

on t4o su;;orts: in ;arti8ular on one i@@ova6le 9in=e su;;ort an5 one

@ova6le 9in=e su;;ort*

Let us analyse <or8es 49i89 a8t on a s9a<t*It is ne8essary to re@e@6er t9at in t9e en=a=e@ent o< strai=9t s;ur

=ears turnin= <or8e F t an5 ra5ial <or8e F 5evelo; ,ra5ial <or8e is al4ays

5ire8te5 to t9e 8entre o< rotation o< t9e =ear/* In t9e en=a=e@ent o<

9eli8al s;ur =ears: 6evel =ears an5 4or@ =earin= 6esi5es turnin= an5

ra5ial <or8es aial <or8e F a 5evelo;s* T9is <or8e is ;arallel to t9e s9a<t

ais* !alues o< @entione5 a6ove <or8es 4ere <oun5 5urin= o< analysis

8orres;on5in= =ear 5rives <or stren=t9*

On t9e 8antilever ;ortion o< t9e s9a<t eit9er a ;ulley: or a s;ro8>et: or

a ;inion: or a 9al< 8ou;lin= @ay 6e @ounte5*

I< a ;ulley or s;ro8>et is installe5 on t9e s9a<t a <or8e a8tin= on t9es9a<t <ro@ t9e si5e o< t9e ele@ent is 5ire8te5 to si5e o< t9e @atin= ;ulley

-.



,s;ro8>et/ alon= t9e 8entre line* T9e value o< t9is <or8e 4as 5eter@ine5

5urin= analysis o< t9e 8orres;on5in= @e89ani8al 5rive*

I< a 9al< 8ou;lin= is installe5 on t9e s9a<t: t9e <irst loa5s t9e s9a<t 6y

t9e torue* A55itionally: 6e8ause o< @isali=n@ent o< s9a<ts oine5 6y t9e8ou;lin= t9e latter eerts u;on t9e s9a<t an a55itional <or8e F c* T9is

<or8e @ay 6e 5ire8te5 to any si5e ,4it9 res;e8t to turnin= <or8e F t /* ?ut

<or analyti8al @o5els 4e 4ill 8onsi5er t9e 4orst 8ase 49en t9is <or8e is

5ire8te5 o;;osite to F t * In t9is 8ase t9e s9a<t 5e<or@ations are

@ai@u@*

hor sin=le sta=e s;ee5 re5u8ers t9e value o< t9is <or8e F c is

5eter@ine5 in t9e <ollo4in= 4ay7

$".c F T = × g49ere T is t9e torue at t9e s9a<t in Nj@*

$#*"*"* Plot t9e analyti8al @o5el o< t9e s9a<t in t9e verti8al ;lane an5

trans<er all <or8es to t9e s9a<t ,hi=* $#*"/* It is ne8essary to note t9at

a88or5in= to t9e t9eoreti8al @e89ani8s as a result o< trans<errin= ;arallel

<or8es to any ;oint t9e a55itional @o@ent 5evelo;s* In our 8ase it is

aial <or8e F a t9at is ;arallel to t9e s9a<t ais* T9at is 49y t9e a55itional

@o@ent is 5eter@ine5 as

"

g

a a

d M = F ×

:

49ere d g is t9e ;it89 8ir8le 5ia@eter o< t9e =ear*

So

33##3%)*- ."*##. $# N @@

"a M = × = × ×

$". $". 3-# "%#%*%N= × = × =c F T

$#*"*3* Deter@ine verti8al su;;ort rea8tin= C? an5 CA * hor t9is ;ur;ose 4e s9oul5 8onsi5er t9e euili6riu@ o< t9e 6ea@ an5 set u;

euations o< @o@ents 4it9 res;e8t to ;oints ? an5 A 7

#2

? M =∑ :#2

A M =∑ *

3++ )3 ."*##. $#+)$*-%Ng

)3 )3

a CA

F a( M ( = =

a(b (

⋅ ⋅ ⋅=

#⋅ ⋅ a C .F a . M ( @a (b= ;# ? M = ∑

-)



#c M = ∑ #g C? a

. @a (b( F b . M =⋅ ⋅3++ )3 ."*##. $#

3)*")Ng)3 )3

a C?

F b . M =

a(b

⋅ ⋅ − ⋅= =

+hor 89e8>in= 4e set u; euation o< <or8es t9at a8t in t9e verti8al

;lane o< t9e s9a<t* T9e su@ o< t9ese <or8es s9oul5 =ive Bero , #2

i F =∑ /*

# Ci F = ∑ #* C? CA . F ( =

3)*") ++ +)$*-% #*. ( =

$#*"*%* Plot t9e 5ia=ra@ o< 6en5in= @o@ents in t9e verti8al ;lane ,2

b M / ,hi=* $#*"/*

g C C? M = 3⋅

# # C M @ = ; 33)*") )3 "*"+ $# N @@ C C? M @a= a ;⋅ = ⋅ = ⋅ ⋅

# g 3 a≤ ≤

ga 3 a ( b≤ ≤ g C C? a M = 3 ( M . F @3 . a⋅ ⋅3 3

3)*") )3 ."*##. $# .%*" $# N @@ C C? a M @a= a ( M ;⋅ = ⋅ + ⋅ = ⋅ ⋅

3

, /

3)*") ,)3 )3/ ."*##. $# ++ )3 #

C C? a M @a b= a b ( M F b

;

+ ⋅ + − ⋅ =

= ⋅ + + ⋅ − ⋅ =$#*"*.* Plot t9e analyti8al @o5el o< t9e s9a<t in t9e 9oriBontal ;lane

an5 trans<er all <or8es to t9e s9a<t ,hi=* $#*"/* In t9is 8ase as a result o<

;arallel trans<errin= <or8e ht t9e torue T 5evelo;s=

3

t

5 3##T h "%)- 3-# $# N @@

" "= × = × = × ×

*

$#*"*)* Deter@ine 9oriBontal su;;ort rea8tin= <or8es G? an5 GA *

hor t9is ;ur;ose 4e s9oul5 set u; euations o< @o@ents 4it9 res;e8t to

;oints ? an5 A 7

#h

? M =∑ :#h

A M =∑ *

--



hor 89e8>in= 4e <in5 t9e su@ o< all <or8es t9at a8ts in t9e 9oriBontal

;lane o< t9e s9a<t* T9is su@ s9oul5 6e eual to Bero , #

h

i F =∑ /*

$#*"*-* Plot t9e 5ia=ra@ o< 6en5in= @o@ents in t9e 9oriBontal ;lane

,

9

6

M/ ,hi=* $#*"/*

$#*"*+* Plot t9e 5ia=ra@ o< total 6en5in= @o@ents ,hi=* $#*"/ ta>in=

into a88ount t9at

-+



$#*"** Plot t9e t4istin= @o@ent 5ia=ra@ ,hi=* $#*"/*

hi=* $#*"* Dia=ra@s o< @o@ents <or t9e s9a<t analyti8al @o5el$#*"*$#* Plot t9e re5u8e5 @o@ents ,hi=* $#*"/ 5ia=ra@ ta>in= into

a88ount t9at H ed

-



$#*"*$$* hor t9e 8riti8al se8tion o< t9e s9a<t ,49ere t9e re5u8e5

@o@ent is @ai@u@/ 4e 89e8> t9e s9a<t <or stati8 stren=t9

[ ]3#*$

σ = ≤ σ×ma3

b b

M

d :

3

3

.#+*# $# "3*."MPa#*$ )#

×σ = =×b

:

"3*." $"#MPa≤

49ere d is t9e 5ia@eter o< t9e s9a<t at t9e 8riti8al se8tiong w bx is t9e

allo4a6le 6en5in= stress* hor steels wbx $"# MPa*


I< wb wbx 4e @ust in8rease t9e 5ia@eter o< t9e s9a<t at t9e 8riti8alse8tion*

$#*3* AnalyBe t9e s9a<t <or <ati=ue stren=t9*

$#*3*$* Deter@ine t9e li@it o< en5uran8e in 6en5in= an5 in torsion

<or t9e s9a<t @aterial7

<or 8ar6on steels7 σ$ #*%3jσul :

<or alloy steels7 σ$ #*3.jσul z $"#:

τ$ ,#*"#*3/jσul :

49ere σul is t9e ulti@ate stren=t9 o< t9e @aterial ,ta6le $#*$/*

In our 8ase <or Steel %#p ,#*%CCr/

$ #*3. +.# $"# %$-*.MPa−σ = × + =

$ #*". +.# "$"*.MPa−τ = × =

$#*3*"* Deter@ine ;ea> @a=nitu5es o< 6en5in= an5 torsion stresses

+#



,σ p: p/ at t9e 8riti8al se8tions o< t9e s9a<t*

Criti8al se8tion is a se8tion 49ere t9e total @o@ent M} is @ai@u@*

It @ay 6e a se8tion 49ere a =ear or a 6earin= is lo8ate5*3

3 3

3%*3" $#M$+*".MPa

#*$ #*$ )#

Σ ×= = =σ× × p

d :3

3 3

T 3-# $##*. #*. %*"+MPa

#*" #*" )#

×= × = × =τ

× × pd :

49ere d is t9e 5ia@eter o< t9e s9a<t at t9e 8riti8al se8tion*

$#*3*3* Deter@ine @ean 8o@;onents o< t9e 6en5in= an5 torsion

stresses ,σm: m/*

I< aial <or8e F a$### N 4e assu@e σm # an5 m p*

Ot9er4ise

"

%

σ =π×

a

m

F

d

: m p**

In our 8ase F a 3%)*- N $### N: so σm # an5 m p %*"+ MPa*

$#*3*%* Deter@ine <a8tors ψ σ an5 ψ τ o< @ean stress 8o@;onents

<or 8ar6on steels ψ σ #*$ an5 ψ τ #*#.g

<or alloy steels ψ σ #*$. an5 ψ τ #*$*

In our 8ase ψ σ #*$. an5 ψ τ #*$*

$#*3*.* Deter@ine e<<e8tive stress 8on8entration <a8tors K σ an5 K *

hor t9is ;ur;ose 4e use ta6le $#*"*

I< t9e 8riti8al se8tion o< t9e s9a<t is a se8tion 49ere a 6earin= is@ounte5 4e 4ill use as stress 8on8entrator inter<eren8e <it* I< a =ear is

installe5 at t9e 8riti8al se8tion a >eye5 ;ortion is 8onsi5ere5 as t9e stress

8on8entrator*

+$



Table 1>.2St&e"" C#n%ent&ati#n /a%t#&" $#& Sha$t"

t

A. Filleted Transitin Regins

=a*e" #$ $i**et &a!i" r

d ma3

Over $+ to 3# $*)

Over 3# to .# "*#

Over .# to +# "*.

Over +# to $"# 3*#

=a*e" #$ K σ

an! K τ

t' 'd $ σ at σ ul ,MPa/ o< $ τ at σ ul ,MPa/ o<

.## -## ## $"## .## -## ## $"##

" #*#$ $*.. $*) $*). $*- $*% $*% $*%. $*%.

#*#" $*+ $* "*# "*$. $*.. $*) $*). $*-

#*#3 $*+ $*. "*#. "*". $*.. $*) $*). $*-

3 #*#$ $* "*# "*$ "*" $*.. $*) $*). $*-.

#*#" $*. "*$ "*" "*% $*) $*- $*-. $*+.#*#3 $*. "*$ "*". "*%. $*). $*- $*-. $*

). =a*e" #$ K σ

an! K τ

$#& 7e,e! +#&ti#n" #$ Sha$t"

σend : MPa $ σ <or >eyseats 8ut

4it9 $ τEn5 @ills Si5e @ills

.## $*)# $*%# $*%#

+"



-## $*# $*.. $*-#

## "*$. $*-# "*#.

$"## "*.# $*# "*%#

C. =a*e" #$ K σ

an! K τ

$#& S+*ine! an! Th&ea!e! P#&ti#n" #$ Sha$t"

σend : MPa

$ σ <or $ τ <or

S;line5

;ortions

T9rea5e5

;ortions

Parallelsi5es

s;lines

Involute

s;lines

T9rea5e5

;ortions

.## $*%. $*+# "*". $*%. $*.#

-## $*)# "*"# "*%. $*.# $*).

## $*-# "*%. "*). $*.. "*$#

$"## $*-. "*# "*+# $*)# "*3

D. =a*e" #$ K σ

K d an! K τ

K d at Inte&$e&en%e;/it J#int"

S9a<t

5ia@eter

d : @@

$ σ $ d at σul : ,MPa/ o< $ τ $ d at σul : ,MPa/ o<

.## -## ## $"## .## -## ## $"##

3# "*. 3*# 3*. %*". $* "*" "*. 3*#

.# 3*#. 3*). %*3 .*" "*". "*) 3*$ 3*)

$## u; 3*3 3*. %*) .*) "*% "*+ 3*" 3*+In our 8ase t9e 8riti8al se8tion o< t9e s9a<t is a se8tion 49ere a

6earin= is @ounte5* So 4e 4ill use as stress 8on8entrator inter<eren8e

<it* T9en

%*3.gσ =d

$

$ "*-τ =

d

$

$ <ro@ t9e ta6le $#*" D*

%## )## M*9 MPa

Kh$*#

#*+

#*)

#*%

$

"

3

%

$#*3*)*

Deter@ine t9e sur<a8e rou=9ness <a8tor $ F * hor t9at 4e use hi=*$#*3*

+3



hi=* $#*3* !alues o< $ F 7 $ ;olis9e5 ;ortionsg " =roun5 ;ortionsg

3 ;ortions @a5e 4it9 <inis9 turnin=g % ;ortions @a5e 4it9 rou=9 turnin=

It is ne8essary to note t9at t9e ;ortion o< t9e s9a<t 49ere a 6earin= is

installe5 s9oul5 6e =roun5 49ile t9e s9a<t ;ortion <or a toot9e5 49eel is@a5e 4it9 <inis9 turnin=*

In our 8ase t9e 8riti8al se8tion is <or t9e ;ortion o< t9e s9a<t 49ere a

6earin= is installe5* T9at is 49y 4e use 8urve " an5 $ F #**

$#*3*-*

Deter@ine <a8tor $ d : 49i89 is use5 to ta>e into a88ount a6solute

5i@ensions o< t9e s9a<t 8rossse8tion* hor t9is ;ur;ose 4e use hi=*$#*%*

hi=* $#*%* !alues o< $ d 7 $ 8ar6on steels 4it9out stress 8on8entratorsg "

alloy steels 4it9out stress 8on8entrators or 8ar6on steels 4it9 stress8on8entrators , $ w"/g 3 alloy steels 4it9 stress 8on8entrators , $ w"/*

I< t9e 8riti8al se8tion is in t9e ;la8e 49ere 6earin= is @ounte5 it is

not ne8essary to 5eter@ine $ d 6e8ause t9e ratio $ σ $ d 4as <oun5

6e<ore , ;*$#*3*./.

$#*3*+* Deter@ine sa<ety <a8tors in ter@s o< 6en5in= an5 torsion

$ d

$*#

#*+

#*)

#*%

3$"

+%



$ %$-*.%*-3

%*3.$+*". #

#*

−σ

σσ

σ= = =× + × × +ψ σ σ

× p m

d F

! $

$ $ g

$ "$"*.$%*)

"*-%*"+ #*$ %*"+

#*

−τ

ττ

τ= = =× + × × + ×ψ τ τ

× p m

d F

! $

$ $ *

$#*3** Deter@ine t9e sa<ety <a8tor o< t9e s9a<t at t9e 8riti8al se8tion

" " xσ τ

σ τ

×= ≥

+! !

! ! ! !

g

" " " "

%*-3 $%*)%*.

%*-3 $%*)

σ τ

σ τ

× ×= = =

+ +! !

! ! !

Allo4a6le values o< t9e sa<ety <a8tor ! x are =iven in ta6le $#*3*

Table 1>.)=a*e" #$ S

De=ree o< a88ura8y o< 5esi=n loa5s: analyti8al@o5els: an5 @e89ani8al 89ara8teristi8s ! x

Hi=9 $*"$*.

A;;roi@ate ,s9a<ts o< @ost =eneral;ur;ose

@e89anis@s/

$*.$*+

Re5u8e5,also <or s9a<ts 4it9 d "## @@/ $*+"*"


+.



11. ANALSIS O/ THE ROLLING CONTACT )EARINGS

Let us analyse t9e rollin= 8onta8t 6earin=s <or stren=t9* Initial

5ates are7 ty;e 5esi=nation o< t9e 6earin= an5 its siBes , an5 d D B/g

rotational s;ee5 n o< t9e 6earin= inner rin=g

8o@;onents o< rea8tin= <or8es in su;;orts 3?: C? % 3A : CA an5 +?g

6asi8 loa5 ratin= A an5 stati8 loa5 ratin= A # <or ra5ial 6all

6earin=s an5 an=ular8onta8t 6earin=s 4it9 ;ressure an=le ~$+ˆ ,ta6les

*3 an5 *%/g

6asi8 loa5 ratin= A an5 aial loa5 ;ara@eter e <or an=ular

8onta8t 6earin=s 4it9 ;ressure an=le ~$+ˆ ,ta6les *% an5 $$*$/g

6asi8 loa5 ratin= A % aial loa5 ;ara@eter e an5 aial loa5 <a8tor

<or ta;ere5 roller 6earin=s ,ta6le *./*

In our 8ase <or t9e out;ut s9a<t 4e 4ill use an=ular8onta8t 6all

6earin=s 3)"$" ,)#$$#""/g n 3*) r;@g 3? %3)3*#% N:

C? 3)*") N: 3A %3+.*3 N: CA +)$*-% N an5 +? F a 3%)*- Ng

A )$*. >N: A # 3*3 >N*

$$*$* Deter@ine t9e total ra5ial rea8tin= <or8es 49i89 a8t on t9e 6earin=s""" "

$ 3)*") %3)3*$ N%3)3*#%= + = + = 3? C? F g""" "

" +)$*-% %3+.*3 N%3##*%%= + = + = 3A CA F *

$$*"* Deter@ine t9e total aial <or8es a8tin= on t9e 6earin=s

$$*"*$* Cal8ulate a55itional aial <or8es ! $ an5 ! " t9at 5evelo; as

a result o< a8tion o< ra5ial <or8es F $ an5 F "

! $ F $⋅eI g ! " F "⋅eI :

49ere eI=e <or ra5ial 6all 6earin=s an5 an=ular 8onta8t 6all 6earin=sg

eI #*+3⋅e <or ta;ere5 roller 6earin=s*

It is ne8essary to note t9at <or ra5ial 6all 6earin=s an5 an=ular

8onta8t 6all 6earin=s 4it9 ;ressure an=le ~$+ˆ aial loa5 ;ara@eter e is

5eter@ine5 6y ta6le $$*$ 5e;en5in= u;on ratio F a 'A o*

+)



In our 8ase F a 'A o=3%)*-33## #*##++g eI=e #*3 ,ta6le $$*$/g

! $ F $⋅eI=%3)3*$j#*3 $3#+*.- Ng ! " F "⋅eI %3+.*3j#*3

$3$.*-+ N*

$$*"*"* Plot t9e analyti8al @o5el o< t9e s9a<t an5 s9o4 all <or8esa8tin= on t9e s9a<t in t9e aial 5ire8tion ,hi=* $$*$/*

hi=* $$*$* hor8es a8tin= on t9e s9a<t in t9e aial 5ire8tion*

Table 11.1=a*e" #$ 9 an! e $#& "#me t,+e" #$ 0ea&ing"

Ty;e o< 6earin=

α° F a 'A o F a ' ,VF /≤e F a,VF /e

e G G

Sin=le

Ro4 ra5ial?all

?earin=

#

#*#$%

$ # #*.)

"*3# #*$

#*#"+ $* #*""#*#.) $*-$ #*")

#*#+% $*.. #*"+

#*$$ $*%. $*3#

#*$- $*3$ #*3%

#*"+ $*$. #*3+

#*%" $*#% #*%"

#*.) $*## #*%%

Sin=le

Ro4An=ular

Conta8t

?all?earin=

$"

#*#$%

$ # #*%.

$*+$ #*3#

#*#" $*)" #*3%

#*#.- $*%) #*3-#*#+) $*3% #*%$

#*$$ $*"" #*%.

#*$- $*$3 #*%+

#*" $*$% #*."

#*%3 $*#$ #*.%

#*.- $*## #*.%

") $ # #*%$ #*+- #*)+

3) $ # #*3- #*)) #*.

F a

! "! $ F a" F a$

×

+-



Sin=le ro4

Ta;ere5 Roller

?earin=

$ # #*% #*%8t=α $*.8t=α

$$*"*3* Deter@ine total aial <or8es F a$ an5 F a"* hor t9at 4e

s9oul5 <in5 t9e su@ F a z ! $ an5 8o@;are 4it9 <or8e ! "* T9ere are 3

;ossi6le 8ases7

i< F a z ! $ ! " F a$ ! $ an5 F a" F a z ! $g

i< F a z ! $ ! " F a$ ! $ an5 F a" ! "g

i< F a z ! $ ! " F a$ ! " F a an5 F a" ! "*

In our 8ase F a z ! $ 3%)*- z $3#+*.- $)..*"- N ! " $3$.*-+

N: t9ere<ore F a$ $3#+*.- N an5 F a" 3%)*- z $3#+*.- $)..*"-N*

$$*3* Deter@ine <a8tor ! 49i89 is use5 to ta>e into a88ount 49at

rin= o< t9e 6earin= is @ova6le*

<or 6earin=s 4it9 @ova6le inner rin= V $g

<or 6earin=s 4it9 @ova6le outer rin= V $*"*

In =eneral ;ur;ose s;ee5 re5u8ers 6earin=s 4it9 @ova6le inner

rin= are use5 only*

$$*%* Deter@ine sa<ety <a8tor $ s 49i89 allo4s <or t9e loa5 nature*

It @ay 6e ran=e5 <ro@ $ to "*. 5e;en5in= u;on t9e ty;e o< 5esi=nin=

@a89ine* hor =eneral ;ur;ose s;ee5 re5u8ers t9e sa<ety <a8tor is

assu@e5 as $*3*

$$*.* Deter@ine te@;erature <a8tor $ t a88or5in= to ta6le $$*"*

Table 11.2=a*e" #$ tem+e&at&e $a%t#& K t

Te@;erature o<

t9e 6earin= t : ˆC$## $". $.# $-. "## "". ".#

$ t $*# $*#. $*$ $*$. $*". $*3. $*%

As a rule in =eneral ;ur;ose s;ee5 re5u8ers t9e 4or>in=

te@;erature o< 6earin=s is less t9an $## ˆC*

$$*)* Deter@ine t9e ra5ial <or8e <a8tor G an5 aial <or8e <a8tor

<or 6ot9 su;;orts* hor t9is ;ur;ose it is ne8essary to <in5 ratio

a

r

i

i

F

V F × <or every su;;ort an5 8o@;are 4it9 aial loa5 ;ara@eter e*

++



I<

a

r

i

i

F e

V F ≤

× t9en G i $ an5 i #* Ot9er4ise G i an5 i are

5eter@ine5 a88or5in= to ta6le $$*$*

In our 8ase7 V $g $ s $*3g $ t $g

$3#+*.-#*3

$ %3)3*$= =

× ×a1

1

F

V F e: t9en

G 1 $ an5 1 #g

$)..*"-#*3--

$ %3+.*3= =

× ×a2

2

F

V F e: t9en G 2 #*%. an5 2

$*+$*

$$*-* Deter@ine t9e euivalent ra5ial loa5s <or 6ot9 su;;orts

P $ , G $⋅V ⋅ F $ z $⋅ F a$/⋅ $ s⋅ $ t ,$j$j%3)3*$z#j$3#+*.-/j$*3j$.)-"*$. N:

P " , G "⋅V ⋅ F " z "⋅ F a"/⋅ $ s⋅ $ t ,#*%.j$j%3+.*3z$*+$j$)..*"-/j$*3j$)%)#*)" N*

$$*+* Deter@ine t9e rate5 li<e in @illion revolutions <or t9e @ost

loa5e5 su;;ort3

)$.##+)"*.

)%)#*)"

= = ÷ ÷

m

ma3

A # =

P :

49ere m 3 <or 6all 6earin=s an5 m

$#

3 <or roller 6earin=s*$$** Deter@ine t9e rate5 li<e in 9ours

6

min

10

60 hh

LL L

n

×= >

× *

hor =eneral ;ur;ose s;ee5 re5u8ers #h @in$"### 9ours*

I< t9e last ineuality is not 8arrie5 out it is ne8essary to resele8t

t9e 6earin= o< @ore 9eavy series an5 @a>e all 8al8ulations on8e @ore*

In our 8ase

6

min

862.59 10153595.1 hours

60 93.6 h

h

L L×

= = >× * Con5ition

is satis<ie5 an5 4e 8an use t9is ty;e o< 6earin=s*

+



1-. DESIGNING THE GEAR SPEED REDUCER

$"*$* Desi=n su;;orts o< t9e s;ee5 re5u8er s9a<ts*

Nor@al o;eration o< 6earin=s 5e;en5s u;on t9e arran=e@ent o< 6earin=s on t9e s9a<t as 4ell as t9e @et9o5 o< <iation o< t9e s9a<t in t9e

aial 5ire8tion*

A88or5in= to <iation o< t9e s9a<t in t9e aial 5ire8tion t9ere are

<ie5 su;;ort an5 <loatin= su;;ort*

De;en5in= u;on arran=e@ent o< 6earin=s 4e 4ill 5istin=uis9

6et4een in4ar5 ,<a8e to <a8e/ arran=e@ent an5 arran=e@ent 4it9 t9e

<ie5 an5 t9e <loatin= su;;orts* So@eti@es out4ar5 ,6a8> to 6a8>/

arran=e@ent o< 6earin=s is use5 too ,<or ea@;le: <or 6evel ;inion

s9a<ts/*

Let us 8onsi5er <eatures o< all arran=e@ents*

In4ar5 arran=e@ent o< 6earin=s*

T9is is t9e @ost ;o;ular arran=e@ent a88or5in= to 49i89 a s9a<t is

<ie5 in t9e aial 5ire8tion in 6ot9 su;;orts* Every su;;ort 4it9stan5s

onesi5e5 aial loa5* T9e inner rin= o< 6ot9 6earin=s rests a=ainst t9e

s9oul5er @a5e on t9e s9a<t or a=ainst t9e en5 <a8e o< ot9er 8o@;onent

installe5 on t9e s9a<t* In its turn: t9e outer rin= o< 6earin=s rests a=ainst

t9e en5 <a8e o< a 8a; or ot9er ;art se8ure5 in t9e 8asin= ,hi=* $"*$/*T9e in4ar5 arran=e@ent is si@;le in 8onstru8tion an5 ;er@its easy

a5ust@ent o< 6earin=s* ?ut t9ere eists a ris> t9at t9e s9a<t 8an 6e

seiBe5 at su;;orts* It is e;laine5 6y t9e <a8t t9at 5urin= o;eration o<

6earin=s: s9a<ts an5 8asin=s 9eat u;* As a result: ra5ial 8learan8es in

6earin=s 5e8rease* Also: t9e s9a<t len=t9 in8reases on 9eatin=: 49i89

re5u8es t9e aial 8learan8e in 6earin=s*

hor sa<e=uar5 a=ainst seiBure 4e s9oul5 ;rovi5e s@all 8learan8e a at

one en5 o< t9e s9a<t 6et4een t9e outer rin= o< t9e 6earin= an5 t9e en5<a8e o< t9e 8a; ,hi=* $"*$: a/* T9is 8learan8e is very s@all ,#*"#*.

@@/* T9at is 49y it is not s9o4n in t9e 5ra4in=* In or5er to a5ust t9is

8learan8e 4e use eit9er t9in @etal s9i@s 1 ;la8e5 6et4een t9e 8asin=

an5 t9e <lan=e5 8a; at one en5 o< t9e s9a<t or a s;a8er rin= installe5

6et4een t9e en5 <a8e o< t9e e@6e55e5 8a; an5 t9e outer rin= o< t9e

6earin=*

In ra5ialt9rust 6earin=s ,an=ular 8onta8t 6all 6earin=s an5 ta;ere5

roller 6earin=s/ t9ere eist ra5ial 8learan8es 6et4een rollin= ele@entsan5 6ot9 rin=s t9at @ay 6e a5uste5 in asse@6ly* ke 8an a89ieve

#



a5ust@ent o< t9ese 8learan8es 6y @eans o< t9in @etal s9i@s$ @ounte5

6et4een t9e 8asin= an5 <lan=es o< 8a;s at 6ot9 en5s o< t9e s9a<t ,hi=*

$"*$: b/* I< 4e 9ave e@6e55e5 8a;s nee5e5 a5ust@ent is a89ieve5 6y

s8re4 $ an5 inter@e5iate 4as9er " ,hi=* $"*"/*

a/

6/

hi= $"*$ In4ar5 arran=e@ent o< 6earin=s7 a ra5ial 6earin=sg b J ra5ial

t9rust 6earin=s

$

$



In t9is 8ase t9e t9rea5e5 ele@ent

si@;li<ies a5ust@ent 6e8ause 8a;s nee5 not 6e re@ove5 to re;la8e t9e

s9i@s 6ut t9e 6earin= asse@6ly 6e8o@es @ore ela6orate*

In4ar5 arran=e@ent o< 6earin=s is use5 <or s9a<ts o< strai=9t s;ur

=ears: 9eli8al s;ur =ears: 6evel =ear an5 4or@ =ear*

?earin=s o< t9e 4or@ s9a<t are arran=e5 as <ie5 an5 <loatin=

su;;orts ,hi=* $"*3/*

T9e <ie5 su;;ort 8onsists o< t4o in4ar5 <a8in= ra5ial t9rust

6earin=s ,as a rule ta;ere5 roller 6earin=s/ @ounte5 in t9e 6earin=

9ousin=* Outer an5 inner rin=s o< t9e <ie5 su;;ort s9oul5 6e <ie5 in 6ot9 aial 5ire8tions* T9at is 49y t9e <ie5 su;;ort 8an 4it9stan5

5ou6lesi5e5 aial loa5* In or5er to a5ust ra5ial 8learan8es in ta;ere5

roller 6earin=s 4e use slotte5 nut ,ta6le $"*$*/ an5 lo8>4as9er ,ta6le

$"*"/*

hloatin= su;;ort is use5 to 8o@;ensate t9er@al 5e<or@ations o< t9e s9a<t an5 @anu<a8turin= errors* ke use as <loatin= su;;ort a ra5ial

"



6all 6earin= 49i89 inner rin= is <ie5 in 6ot9 aial 5ire8tions an5 outer

rin= is le<t <ree* hor <iation o< t9e inner rin= 4e e@;loy eit9er en5

;lates ,ta6le $3*3: $3*%/: or slotte5 nuts 4it9 lo8> 4as9ers: or s;rin=

rin=*T9e ri=9tness o< t9e 4or@ en=a=e@ent is a5uste5 6y @eans o<

@etal s9i@s 1 ,hi=* $"*3/ @ounte5 6et4een t9e 8asin= an5 t9e <lan=e o<

t9e 9ousin=*

Su;;orts o< t9e 6evel ;inion s9a<t are installe5 in t9e 9ousin= a88or5in=

to out4ar5 arran=e@ent ,hi=* $"*%/* In t9is 8ase 4e o6tain t9e @ini@u@

6en5in= @o@ent 5evelo;in= on t9e s9a<t* In or5er to a5ust ra5ial

8learan8es in 6earin=s 4e s9oul5 use a slotte5 nut 4it9 a lo8>4as9er*

Ri=9tness o< t9e 6evel =ear en=a=e@ent is a5uste5 6y @etal s9i@s 1

,hi=* $"*%/ @ounte5 6et4een t9e 8asin= an5 t9e 9ousin= <lan=e*

Table 12.1

Stan!a&! "*#tte! nt" GOST 11B1;F

3



Table 12.2Stan!a&! *#% a"he&" GOST 11B-;F

%

T9rea5 5ia@eter: 5 T9rea5 ;it89 D D$ H 6 9

"#

$*.

3% "- +

. "*.

"" 3 3#

$#

"% %" 33"- %. 3)

3# %+ 333 ." %"3) .) %.

) 33 )# %+%" ). ."%. -# .)%+ -. )#

$" + %." +# )..)

"

+. -#)# # -.

)% . +#)+ $## +.

$. $# .-" $#. #-) $$# .+# $$. $##



.



Table 12.)

Dimen"i#n" #$ S*#t" Re%ei'ing L#% (a"he&

Ta0"9 mm

)

T9rea55ia@eter 5$ 5" 53 6 S l

9

Not

less

Not

@ore

"# "#*. 3- "-

%*+ $*#

$-

3*. )*#"" ""*. %# 3# $"% "%*. %% 33 "$"- "-*. %- 3) "%

%*. +*#

3# 3#*. .# 3 "-33 33*. .% %"

.*+

$*)

3#3) 3)*. .+ %. 333 3*. )" %+ 3)%" %"*. )- ." 3%. %.*. -" .) %"%+ %+*. -- )#

-*+

%.." ."*. +" ). %

.*. $#*#.) .- +- -# .3)# )$ " -. .-)% ). - +# )$)+ ) $#" +.

*.

).

)*. $3*#-" -3 $#- # )-) -- $$" . -3+# +$ $$- $## -)

T9rea55ia@eter

d% mm

a$ a"min a3min a%min d $min

"# ) " 3*. $*# $)*.

"" ) " 3*. $*# $+*.

"- ) 3 %*# $*. "3*.

3# ) 3 %*# $*. ")*.

33 ) 3 %*# $*. "*.

3) ) 3 %*# $*. 3"*.

3 ) 3 %*# $*. 3.*.%" + 3 .*# $*. 3+*.



hi= $"*%* Out4ar5 arran=e@ent o< 6earin=s o<t9e 6evel ;inion s9a<t $"*"* Deter@ine

5i@ensions o< ele@ents t9at are a ;art o< t9e su;;ort asse@6lies*

$"*"*$* ?earin= 8a;s*

?earin= 8a;s @ay 6e @a5e 4it9 s8re4s or e@6e55e5 in t9e 8asin=*Constru8tion o< t9e s8re4 8a; an5 its 5i@ensions are =iven in hi=* $"*.

a% 49ere d k is 5eter@ine5 a88or5in= to ta6le $"*%* I< 6earin=s are 9el5 in

;la8e 4it9 nuts or s;rin= 4as9ers: 8onve 8a;s are use5 ,hi=* $"*.: 8/*

I< t9e len=t9 o< t9e 8a; sleeve ;er@its: a =roove is @a5e in t9e

sleeve: in 49i89 a roun5se8tion ;a8>in= rin= o< =asoline or oil

resistant ru66er is <itte5 ,hi=* $"*.: 6/* T9e =roove ;ro<ile is s9o4n in

hi=* $"*.: 6 an5 t9e 5i@ensions o< its 6asi8 ele@ents are ta>en as

<ollo4s7 b .*) @@ an5 d $ D -*% @@* T9e 8rossse8tion 5ia@eter isassu@e5 as d %*) @@*

-



hi=*$"*.* ?earin= s8re4 8a;s

Da= D (/8d K

a

b

c

Table 12.*S%&e" $#& $a"tening 0ea&ing %a+"

Constru8tions o< e@6e55e5 8a;s are =iven in hi=* $"*) 49ere ‹ is

5eter@ine5 a88or5in= to ta6le $"*.: b ≈ ‹: c ≈ #*.8‹ * T9ese 8a;s reuire

no s;e8ial atta89@ent to t9e 8asin=: so no 9oles in t9e 8a;s: t9rea5e5

9oles in t9e 8asin=: or s8re4s are nee5e5* Ho4ever: 8a;s o< t9is

8onstru8tion @ay only 6e use5 49ere t9e oint 6et4een t9e 8asin= an5

t9e 8over lies in t9e ;lane o< t9e s9a<t ais* ?esi5es: 6earin= asse@6lies

+

D: @@ d k Nu@6er o< s8re4s

To -. M+ %

+#. M$# %

$##$%# M$# )

$.#"$. M$" )

"".3)# M$) )



4it9 e@6e55e5 8a;s 6e8o@e @ore ela6orate in s9a;e* It is e;laine5 6y

ne8essity to a5ust ra5ial 8learan8es in t9e 6earin=*

Table12./

Thi%ne"" #$ the em0e!!e! %a+

D: @@ .#)" )3. $##$%. $.#""#

L: @@ . ) - +

$"*"*"*?earin= 9ousin=

Constru8tions o< 6earin= 9ousin=s an5 t9eir 5i@ensions are =iven in

ta6le $"*)*

Table 12.0

)ea&ing h#"ing"

D: @@ .# .#+# +#$"# $"#$-#

‹: @@ %. )+ +$# $#$"*.

b: @@ 3 . . +

D$ Daz.d hg c … d hg h ,$*#$*"/d h g ‹$ … ‹g ‹" … $*"‹:

49ere d h is 5ia@eter o< t9e 9ole <or a s8re4 <ro@ ta6le $"*-



Table 12.4Diamete&" #$ h#*e" $#& 0#*t"9 mm

?olt 5ia@eter M$# M$" M$) M"# M"% M3# M3)

Hole 5ia@eters <or an89or 6olts $. $ "% "+ 3. %"Hole 5ia@eter <or tie 6olts $$ $% $+ "" ") 33

$"*3* Desi=nin= 8asin=s*

Casin=s are use5 to su;;ort toruetrans@itte5 ele@ents in 5esi=n

;osition an5 ta>e u; loa5s 5evelo;e5 in s;ee5 re5u8ers 5urin=

o;eration* T9e @ain @aterial o< 8asin=s is 8astiron*

A 8asin= @ust 6e ri=i5 to ;revent s9a<t @isali=n@ent un5er internal

an5 eternal loa5s* T9is 8an 6e a89ieve5 6y usin= sti<<enin= ri6s t9at

also 8arry out t9e <un8tion o< 8oolin= <ins*Casin= @ay 9ave s;lit or sin=le;ea8e 8onstru8tion* hor s;lit

8onstru8tions t9e oint 6et4een a 8asin= an5 a 8over is usually ;rovi5e5

in t9e ;lane ;arallel to t9e 6ase an5 t9at ;asses t9rou=9 t9e ais o<

rotation o< 8orres;on5in= =ears*

T9e @ain 5i@ensions o< t9e 8asin= ,hi=* $"*-/7

$"*3*$* Casin= an5 8over 4all t9i8>ness7

<or sin=le sta=e s;ur =ear s;ee5 re5u8er δ #*#".ja& z$ ≥ + @@g <or sin=le sta=e 6evel =ear s;ee5 re5u8er δ #*#.j e z$ ≥ + @@g

<or sin=le sta=e 4or@ =ear s;ee5 re5u8er δ #*#%ja& z % ≥ + @@:

49ere a& is t9e 8entre 5istan8e: e is outer 8one 5istan8e*

$"*3*"* hlan=e t9i8>ness at t9e oint ;lane

b $*.jδ*

$"*3*3* T9i8>ness o< t9e <lan=e <or 8onne8tion to a <ra@e

p "*3.jδ*$"*3*%* T9i8>ness o< t9e ri6

m ,#*+$*#/jδ*

$"*3*.* Dia@eter o< t9e an89or 6olt

d $ ,#*#3#*#3)/ja&z$":

d $ #*#-"j ez$"*

O6taine5 @a=nitu5e o< d $ s9oul5 6e roun5e5 o<< to t9e nearest

=reater si5e a88or5in= to stan5ar5 series =iven in ta6le $"**

$"*3*)* Nu@6er o< an89or 6olts

$##



+ #*##.j, ##z B#/ ≥ %:

49ere B# is t9e 4i5t9 o< t9e s;ee5 re5u8er 6aseg ## is t9e len=t9 o< t9e

s;ee5 re5u8er 6ase* It is ne8essary to note t9at t9e nu@6er o< an89or

6olts s9oul5 6e al4ays even*

$"*3*-* Dia@eter o< t9e tie6olt near 6earin=s

d " ,#*-#*-./jd $*

O6taine5 value o< d " s9oul5 8orres;on5 to stan5ar5 value ,ta6le $"*/*

$"*3*+* Dia@eter o< tie 6olts t9at 8onne8t t9e 8asin= an5 t9e 8over

<lan=es

d 3 ,#*.#*)/jd $*

Roun5 o<< o6taine5 value o< d 3 to t9e =reater si5e a88or5in= tostan5ar5 series ,ta6le $"*/*

$"*3** Distan8e 6et4een tie6olts o< 5ia@eter d 3 l ,$#$"/jd 3*

$"*3*$#* Dis;osition o< 6olts on t9e <lan=e ,hi=/

3 ,$$*"/jd 9ole:

C δ z e:

49ere d 9ole is t9e 5ia@eter o< t9e 9ole <or <ittin= t9e 6olt ,ta6le $"*-/ge is t9e 5istan8e t9at allo4s to =ri; t9e 6olt 9ea5 6y a s;anner

,ta6le$"*+/*

Table 12.5=a*e #$ e

Dia@eter o< t9e 6olt M$# M$" M$) M"# M"%

e: @@ $3 $% $) "# "%

$"*3*$$* Hei=9t o< t9e 6oss is 5eter@ine5 <ro@ stru8tural

8onsi5eration ta>in= into a88ount t9e <ollo4in= reuire@ent

≥ #*.jd " z d k :

49ere d k is t9e 5ia@eter o< t9e 6olt: t9at 8onne8ts t9e 6earin= 8a; 4it9

t9e 8asin= ,ta6le$"*%/*

$#$



$"*3*$"* Di@ensions o< 6olts: nuts an5 4as9ers are =iven in ta6les

$"* $"*$$* T9e len=t9 an5 t9rea5e5 len=t9 o< t9e 6olt are =iven in ta6le

$#"



$"*$"* En=a=e5 len=t9 o< t9e 6olt: t9e 5e;t9 o< t9e 9ole an5 t9rea5e5

len=t9 o< t9e 9ole are 5eter@ine5 a88or5in= to ta6le $"*$3*

$"*3*$3* In or5er to 9ol5 to=et9er t9e 8asin= an5 t9e 8over an5 to

;revent t9eir relative @ove@ent in aial 5ire8tion t4o ;ins are use5*T9ey are ;la8e5 alon= t9e <lan=e 5ia=onal* T9e 5ia@eter o< t9e ;in is

5eter@ine5 as d ;in #*.jd $*

$"*3*$%* hor transition an5 installation t9e 8over an5 t9e 8asin=

s9oul5 6e @a5e 4it9 li<tin= eye6olts ,ta6le $"*$%/ or eyes an5 loa5

9oo>s ,hi=* $"*+/*

$*.q‹g 3q‹g d 3q‹g a ,$*"$*./q‹g s ,"3/q‹hi=*$"*+* Loa5 eyes an5 9oo>s

$"*3*$.* hor =ear ins;e8tion an5 lu6ri8ation an ins;e8tion 9ole is ;rovi5e5 in t9e u;;er ;ortion o< t9e 8over* T9e 8over o< t9e ins;e8tion

9ole is 5eter@ine5 a88or5in= to ta6le $"*$.*

$"*3*$)* Durin= o;eration: ;ressure insi5e a 8asin= in8reases 5ue to

9eatin= o< t9e oil an5 air* As a result t9e lu6ri8ant is ee8te5 outsi5e

t9rou=9 seals an5 oints* To avoi5 t9is <a8t airvents are ;rovi5e5 in t9e

to; ;ortion o< t9e 8asin= <or 8onne8tion 6et4een t9e inner s;a8e an5 t9e

environ@ent* Possi6le 8onstru8tions o< airvents are =iven in ta6les $"*$)

an5 $"*$-*

$"*3*$-* hor 5rainin= t9e oil 4it9 =rit an5 ot9er 5e6ris a 5rain 9ole is

@a5e in t9e 8asin= 6otto@: 49i89 is sto;;e5 4it9 a ;lu= 4it9 eit9er

strai=9t or ta;er t9rea5 ,ta6le $"*$+/*

$"*3*$+* T9e level o< t9e oil 8ontaine5 in t9e s;ee5re5u8er 8asin= is

89e8>e5 4it9 oil =au=es o< various 8onstru8tions* A@on= t9e@ t9ere are

5i; sti8>s ,ta6le $"*$/ or trans;arent tu6e =au=es* ,ta6le $"*"#/*

h i = * $

" * - * C o n s t r u 8 t i v e e l e @ e n t s a n 5 t 9 e i r 5 i @

e n s i o n s o < t 9 e 8 a s i n =

h i = * $

" * - *

C a s i n = a n 5 8

o v e r o < t 9 e s ; e e 5 r e 5 u 8 e r

$#3



Table 12.6Stan!a&! 0#*t" GOST BB;BF

Para@eter T9rea5 5ia@eter d% @@

) + $# $" $) "# "% 3#

T9rea5 ;it89:@@

$*# $*". $*. $*-. "*# "*. 3*# 3*.

Ra5ius : @@

not @ore#*) $*$ $*$ $*) $*) "*" "*" "*.

Dia@eter D%

@@

$$ $%*. $ "$ "- 33*. %#*. .#*

S;an !% @@ $# $3 $- $ "% 3# 3) %)

Hei=9t "% @@ %*. .*. - + $# $3 $. $+*-

Table 12.1>Stan!a&! nt" GOST <1<;BF


) + $# $" $) "# "% 3# 3)

T9rea5 ;it89: @@ $*# $*". $*. $*-. "*# "*. 3*# 3*. %*#

Dia@eter D: @@

near

$$ $%*. $ "$ "- 33*. %#*. .$*. )"

S;an !% @@ $# $3 $- $ "% 3# 3) %) ..

Hei=9t "% @@ . )*. + $# $3 $) $ "% "

$#%



Table 12.11Stan!a&! "+&ing a"he&" GOST >5-;BF

Para@eter T9rea5 5ia@eter d : @@

) + $# $" $) "# ". 3# 3)Dia@eter d #: @@ )*$ +*" $#*" $"*" $)*3 "#*. "%*. 3#*. 3)*.

T9i8>ness s% @@ $*% "*# "*. 3*# 3*. %*. .*. )*. +*#

Table 12.12)#*t an! "%&e *ength9 mm

d # l # d # l #

+""

$##***3#g

".***+

#l $)

%%

3##***$)#g

3+

$.#***%+g

%#***"#

#l

$#3"

"##***$)#g

")

$.#***3.g

3#***$#

#l "#

."

3##***$)#g

%)

$.#***..g

.#***".

#l

$"3)

")#***$)#g

3#

$.#***3.g

3#***$%

#l "%

)#

3##***$)#g

.%

$.#***).g

)#***3.

#l

?olt len=t9 s9oul5 6e 89osen <ro@ t9e <ollo4in= stan5ar5 series: @@7

+: $#: $": $%: $): "#: ".: 3#: 3.: %#: %.: .#: ..: )#: ).: -#: -.: +#: #:

$##: $$#: $"#: $3#: $%#: $.#: $)#: $-#: $#: "##: ""#: "%#: ")#: 3##*

$#.



Table 12.1)Dimen"i#n" #$ 0#*t #int"


) + $# $" $) "# "%

a: not less $*".j5

a1: not less 3*. % %*. .*. ) - +

a2: not less " "*. 3 3*. % . )

a): not less ) + $$ $" $. $+

a* $*. $*. " " "*. "*. 3

c $ $*) $*) $*) " "*. "*. D1 $. $+ "" 3# 3. %"

D2 $+ "" ". 3# 3+ %.

Table 12.1*Li$ting e,e;0#*t"9 mm GOST 5B<1;B3F

$#)



$#-

d d 1 d 2 h h1 l - c 3M+ 3) "# $+ ) $+

"

$*" "*.

M$# %. ". "" + "$ $*. 3

M$" .% 3# ") $# ". $*+* 3*.

M$) )3 3. 3# $" 3" " %



Table 12.1/In"+e%ti#n h#*e %#'e&

?

@@

B

@@

?1

@@

B1

@@

A

@

@

A 1@@

$

@

@

@

@

Di@ension

s o< s8re4

Nu@6er

o< s8re4s

$## -. $.# $## $". $## $" M+"" %

$.# $## "## $.# $-. $". $" M+"" %

"## $.# ".# "## "3# $3# $+" $. M$#"" )

Table 12.10 Ai& 'ent9 mm

d d 1 d 2 D h l a " 1 " 2 a1

M$"$*-

.

$" "# 3" %# $" .*. " "% $3

M$)" $) ". %# .# $) - 3. 3# $)

$#+



$#



Table 12.14 Ai& 'ent9 mm

d D l l 1 d 1 a s

M$"$*". $) $ $# % " $-

M$)$*. "" "3 $" . " ""

M"#$*. 3# "+ $. ) % ""

Table 12.15P*g" $#& !&ain h#*e"9 mm

d b m a # D s l

M$"$*"

.$" +

3

"3 ") $*- $*)

M$)$*.$.

"+ 3#"" "%*%

M"#$*. $# " 3"

$$#



Table 12.16Di+ "ti%"9 mm

d d 1 T9rea5 ;it89 d 2 D l 1 l 2 #

3 $# $*# $) "# $# $" $)

% $" $*". "# ". $" $. "#

) $) $*. ". 3" $. $. ".

Table 12.2>

T&an"+a&ent t0e gage9 mm

$$$

d D D1 #

3# )# %+ $"

.# +" -# $%*.



$"*%* Desi=nin= lu6ri8ation syste@ o< t9e s;ee5 re5u8er*

Lu6ri8ation serves to 5e8rease <ri8tional loses: to o<<er ;rote8tion

a=ainst 8orrosion an5 to i@;rove s;ee5 re5u8er o;eration* T9e usual

lu6ri8ants <or @es9in= ele@ents: 6earin=s o< t9e s;ee5 re5u8er are@ineral an5 synt9eti8 oils an5 =reases*

T9e 6asi8 ;ara@eter o< any oil is its vis8osity t9at 89ara8teriBes t9e

a6ility o< <lui5 layers to resist <lo4* T9e oil vis8osity is 89osen

5e;en5in= u;on t9e e;e8te5 ;eri;9eral s;ee5: loa5 an5 toot9 @aterials*

It s9oul5 6e raise5 4it9 in8reasin= loa5 an5 5e8reasin= s;ee5* T9e oil

vis8osity is 5eter@ine5 a88or5in= to ta6les $"*"$an5 $"*""* T9e oil is

89osen 6y ta6le $"*"3*

Table 12.21Re%#mmen!e! 'i"%#"it, #$ #i*" $#& *0&i%ating gea&ing hen t<

°

C

Conta8t stresses : σ " : MPa

Kine@ati8 vis8osity: $#) at ;eri;9eral s;ee5 V : @se8

U; to " Over " to . Over .

U; to )## 3% "+ ""

Over )## to $### )# .# %#

Over $### to "### -# )# .#

Table 12.22Re%#mmen!e! 'i"%#"it, #$ #i*" $#& *0&i%ating #&m gea&" hen

t1°C

Conta8t stresses : σ " : MPaKine@ati8 vis8osity: $#) at ;eri;9eral s;ee5 V : @se8

U; to " Over " to . Over .

U; to "## ". "# $.Over "## to ".# 3" ". $+

Over ".# to 3## %# 3# "3

T9ere are t4o @et9o5s o< lu6ri8ation7

i@@ersion lu6ri8ation: 49en toot9e5 49eels are i@@erse5 into

t9e oil 6at9g

strea@ lu6ri8ation: 49en oil <ee5s t9e 8onta8t area o< toot9e5

49eels 6y @eans o< s;e8ial noBBles*

$$"



Table 12.2)Re%#mmen!e! #i* g&a!e" $#& gene&a*;+&+#"e "+ee! &e!%e&

Oil Oil =ra5e Kine@ati8 vis8osity: $#

)

^

"

W

In5ustrial

at .#°

‘$"A $#$%

‘"#A $-"3

‘".A "%"-

‘3# "+33

‘%#A 3.%.

‘.#A %-..

‘-#A ).-.

‘$##A #$$+Aviation

at $##°C

2$% $%

2("" ""

2"# "#*.

I@@ersion lu6ri8ation is e<<e8tive 49en ;eri;9eral s;ee5 is less t9an

$# @se8*

T9e oil 6at9 lu6ri8ates t9e lar=er 49eel* T9e re8o@@en5e5 5e;t9 o<

i@@ersion o< t9e s;ur =ear ran=es <ro@ m to .jm 6ut not less t9an $#@@ ,m is t9e @o5ule o< t9e =earin=/* ?evel =ears are i@@erse5 alon=

t9e entire len=t9 o< a toot9*

In 4or@5o4n s;ee5 re5u8ers t9e oil level s9oul5 not e8ee5 t9e

t9rea5 9ei=9t o< t9e 4or@* ?ut in t9is 8ase t9e oil level s9oul5 not rise

a6ove t9e 8entre o< t9e lo4er rollin= ele@ent o< t9e 4or@ s9a<t

6earin=s* I< t9e 4or@ is not i@@erse5 in oil t9e a55itional rin=s 4it9

6la5es are use5 ,hi=* $"*/* In 4or@u; arran=e@ent t9e 4or@ =ear

s9oul5 6e i@@erse5 not @ore t9an $3 o< t9e 4or@ =ear ra5ius*

Let us 5eter@ine t9e volu@e o< t9e oil 6at9* Nee5e5 volu@e is 89osen to ensure re@ovin= t9e 9eat =enerate5 in

t9e en=a=e@ent o< a =earin= to 8asin= 4alls* Re8o@@en5e5 volu@e o<

t9e oil 6at9 is 89osen as #*3. to #*- liter o< t9e oil ;er $ >ilo4att o<

trans@itte5 ;o4er* Conseuently: t9e nee5e5 volu@e

V = ,#*3.#*-/q P @otor *

$$3



hi=* $"** R in= 4it9 6la5es

T9e lar=er volu@e 8orres;on5s to t9e lon=er oil li<e an5 6etter lu6ri8ation 8on5itions* T9at is 49y t9e volu@e o< t9e oil 6at9 is only

li@ite5 6y t9e @ai@u@ ;er@issi6le oil level in t9e 8asin=*

T9e 5istan8e 6et4een t9e oil level an5 t9e s;ee5 re5u8er 6otto@ is

5eter@ine5 as

V " =

! : 49ere ! = #⋅ B is t9e area o< t9e s;ee5 re5u8er

inner s;a8e in 5@"g # an5 B are 8orres;on5in=ly t9e len=t9 an5 t9e

4i5t9 o< t9e s;ee5 re5u8er inner s;a8e in 5@* It is ne8essary to note t9at

t9e @ini@u@ 5istan8e 6et4een to;s o< teet9 o< t9e lar=er =ear an5 t9es;ee5 re5u8er 6otto@ is "# @@*

Lu6ri8ation o< 6earin=s*

?earin=s @ay 6e lu6ri8ate5 4it9 t9e sa@e oil as use5 <or t9e

@as9in= ;arts ,49en t9e ;eri;9eral s;ee5 is =reater t9an 3 @se8/ or

in5ivi5ually 4it9 =reases*

S;las9 lu6ri8ation is use5

49en t9e 6earin=s are installe5

in 8ases 49i89 are not insulate5

D ≈ D

6 e a r i n = e H t e r n a l

hi=* $"*$#* ?earin=s 4it9 s9iel5s

$$%



<ro@ t9e =eneral syste@ o< lu6ri8ation unit* Rotatin= ;arts ,=ears:

49eels et8*/ 8o@e into 8onta8t 4it9 oil 49i89 <ills in into t9e 9ousin=

t9en un5er rotation s;rays oil: 49i89 <alls on t9e rollin= 6o5ies an5

6earin= tra8>s*To ;rote8t t9e 6earin=s <ro@

t9e 9eavy ets o< oil ,49i89 8reate

9i=9s;ee5 9eli8al ;inions or

4or@s/ t9e s9iel5s ,;rote8tive

4as9ers/ are installe5 ,hi=*

$"*$#/*

Pressure lu6ri8ation t9rou=9

noBBles is use5 <or re5u8ers:

4or>in= <or a lon= ti@e 4it9out interru;tion: as 4ell as <or t9e 6earin=s

o< 9i=9s;ee5 trans@ission: 49i89 is ne8essary to ;rovi5e intensive 9eat

re@oval*

Oil <o= lu6ri8ation is use5 <or 9i=9s;ee5 un5erstresse5 6earin=s*

T9is @et9o5 allo4s to ;enetrate t9e oil in t9e 6earin=s: lo8ate5 in

ina88essi6le ;la8es: 8reates a <lo4 4it9 @ini@al lu6ri8ation oil

8onsu@;tion ;rovi5es a =oo5 8oolin= o< 6earin=s an5 t9e ;ressure

;rote8ts t9e asse@6ly <ro@ 8onta@ination*

Greases o<<er 6etter ;rote8tion a=ainst 8orrosion t9an oils an5 it†suse5 49en environ@ent 8ontains 9ar@<ul i@;urities or t9e te@;erature

s9ar;ly 89an=es* In t9is 8ase =reaseretainin= rin=s ,hi= $"*$$/ are use5

to isolate t9e 6earin= 8avity <ro@ t9e inner s;a8e o< t9e 8asin=* T9e rin=

;eri;9ery s9oul5 eten5 over t9e en5 <a8e o< t9e 6earin= 9ousin= <or $

or " @@ ,hi=* $"*$"/* T9e =a; 6et4een t9e rin= ;eri;9ery an5 t9ehi=* $"*$$* Greaseretainin= rin= hi=* $"*$" ?earin= asse@6ly 4it9 =rease

8u;

$$.



9ousin= s9oul5 6e a6out #*" @@* T9e rin= rotates to=et9er 4it9 t9e

s9a<ts an5 it 9as <ro@ t4o to <our =rooves* In or5er to <ee5 t9e =rease

insi5e t9e 6earin= 4it9out re@ovin= t9e 8a; =rease 8u;s are use5

,hi=*$"*$"/* T9e lu6ri8ant is ine8te5 un5er ;ressure 6y @eans o< a=rease =un*

$"*.* Analysis o< >eye5 oints*

Di@ensions o< >eys are 89osen a88or5in= to ta6le $"*"% 5e;en5in=

u;on t9e s9a<t 5ia@eter* T9e len=t9 o< t9e >ey s9oul5 6e less t9an t9e

9u6 len=t9 6y .$# @@ an5 8orres;on5s to t9e stan5ar5 series*

In =eneral;ur;ose s;ee5 re5u8er: >eye5 oints are usually analyBe5

to ;revent 6earin= stresses*

[ ]$

"

, /

×σ = ≤ σ

× − ×bea bea

d

T

d h t l :

49ere T is t9e torue in Nj@@g d is t9e 5ia@eter o< t9e s9a<t in @@g h is

t9e 9ei=9t o< t9e >ey in @@g t $ is t9e 5e;t9 o< t9e slot in t9e s9a<tg l d is

t9e 5esi=n len=t9 o< t9e >ey in @@ ,<or >eys 4it9 roun5 si5es l d l bg

<or >eys 4it9 suare si5es l d l : 49ere l is t9e len=t9 o< t9e >eyg b is t9e

4i5t9 o< t9e >ey/g wbea x is t9e allo4a6le 6earin= stress ,<or 8astiron

9u6s wbea x)#+# MPag <or steel 9u6s wbea x$##$"# MPa/*

Table 12.2*

$$)



*!

Stan!a&! Sn 7e,"

S9a<t 5ia@eter d :

@@

Key 8ross

se8tion: @@Keyseat 5e;t9: @@

Len=t9 l

b h s9a<t: t $ 9u6: t "Over $- to "" ) ) 3*. "*+ Over $% to -#

Over "" to 3# + - % 3*3 Over $+ to #

Over 3# to 3+ $# + . 3*3 Over "" to $$#Over 3+ to %% $" + . 3*3 Over "+ to $%#

Over %% to .# $% .*. 3*+ Over 3) to $)#

Over .# to .+ $) $# ) %*3 Over %. to $+#

Over .+ to ). $+ $$ - %*% Over .# to "##

Over ). to -. "# $" -*. %* Over .) to ""#

Over -. to +. "" $% .*% Over )3 to ".#

Over +. to . ". $% .*% Over -# to "+#

Over . to $$# "+ $) $# )*% Over +# to 3"#

Over $$# to $3# 3" $+ $$ -*% Over # to 3)# Note7 T9e len=t9 o< t9e >ey is 89osen a88or5in= to t9e <ollo4in= series7 )g

+g $#g $"g $%g $)g $+g "#g ".g "+g 3"g 3.g %#g %.g .#g .)g )3g -#g +#g #g $##g

$$#g $".g $%#g $)#g $+#g "##*

$$-



13. DESIGNING THE MECHANICAL DRI=E

A @e89ani8al 5rive is 5ra4n in t4o ;roe8tions ,as a rule: <ront

vie4 an5 to; vie4/ to s8ale $7 % or $7.*

$3*$* Dra4 t9e @ain stru8tural units o< t9e @e89ani8al 5rive*A@on= t9e@ t9ere is ele8tri8al @otor ,ta6le *$/: 8ou;lin= 4it9 ru66er

6us9e5 stu5s ,ta6les *-/: 6elt 5rive: s;ee5 re5u8er: o;en =earin=: 89ain

5rive* Di@ensions o< all @entione5 a6ove ele@ents an5 units 9ave 6een

<oun5*

$3*"* Desi=n t9e out;ut s9a<t o< t9e @e89ani8al 5rive ,hi=*$3*$/*

hi=*$3*$* Out;ut s9a<t o< t9e @e89ani8al 5rive

Deter@ine t9e @ini@u@ 5ia@eter o< t9e out;ut s9a<t* hor t9is

;ur;ose 4e use t9e sa@e <or@ula as <or t9e s;ee5 re5u8er s9a<ts

3@in

#*" x

T d =

× τ*I< t9e out;ut s9a<t o< t9e @e89ani8al 5rive is oine5 4it9 t9e s;ee5

re5u8er s9a<t 6y t9e 8ou;lin=: t9e @ini@u@ 5ia@eter o< t9e @e89ani8al

5rive out;ut s9a<t is eual to t9e @ini@u@ 5ia@eter o< t9e s;ee5 re5u8er

out;ut s9a<t*

On t9e 8antilever ;ortion o< t9e out;ut s9a<t 9al< 8ou;lin=:

s;ro8>et or =ear @ay 6e @ounte5* T9ey s9oul5 6e <ie5 in t9e aial

5ire8tion* T9at is 49y it is ne8essary to ;rovi5e t9e s9oul5er on t9e

s9a<t* T9en t9e 5ia@eter o< t9e se8on5 ;ortion o< t9e s9a<t is 5eter@ine5

as d "d $ z "qt $ ,t $ is 89osen <ro@ ta6le *"/*

$$+



T9e se8on5 ;ortion o< t9e out;ut s9a<t is <or @ountin= a 6earin=*

T9at is 49y t9e 5ia@eter o< t9is ;ortion s9oul5 6e en5e5 6y # or .*

T9e net ;ortion o< t9e out;ut s9a<t is ne8essary <or installation o<

t9e 5ru@ or 8onveyer s;ro8>ets* Dia@eter o< t9is ;ortion is d 3 d " z "qt $*T9e last ;ortion o< t9e out;ut s9a<t is <or @ountin= t9e se8on5

6earin=* T9e 5ia@eter o< t9is ;ortion is d "*

$3*3* Desi=n su;;orts o< t9e out;ut s9a<t*

As a rule: su;;orts o< t9e out;ut s9a<t are @ounte5 in 5i<<erent

9ousin=s* In or5er to 8o@;ensate ina88ura8y an5 @isali=n@ent in

asse@6ly sel<ali=nin= 5ou6lero4 s;9eri8al ra5ial 6all 6earin=s o< t9e

li=9t4ei=9t series are use5 ,ta6le $3*$/* O4in= to t9e ra8e s;9eri8al

sur<a8e o< t9e outer rin=: t9ese 6earin=s 8an 9an5le t9e s9a<t @isali=n@ent

o< u; to " or even 3*

Table 1).1D#0*e;&# &a!ia* 0a** 0ea&ing" GOST -5-;F.

Lighteight "e&ie"9 mm

d c #*.j, Dzd /

D& #*".j, Dd /

! #*$-j, Dd /

Ty;e5esi=n

ation

d D B A :

>N

A #:

>N

<or

e

a

F

F

e

a

F

F e

#

$"#% "# %- $% $*. *. 3*$+ #*"- "*3$ 3*.- "*%"

$"#. ". ." $. $*. $"*$ %*# #*"- "*3" 3*) "*%%

$"#) 3# )" $) $*. $.*) .*+ #*"% "*.+ 3* "*-

$"#- 3. -" $- " $.* )*) #*"3 "*-% %*"% "*+-

$"#+ %# +# $+ " $*# +*.. #*"" "*+- %*%% 3*#$

$"# %. +. $ " "$*) *). #*"$ "*- %*) 3*$$

$"$# .# # "# " ""* $#*+ #*"$ 3*$3 %*+. 3*"+

$"$$ .. $## "$ "*. ")*. $3*3 #*" 3*"3 .*# 3*3

$"$" )# $$# "" "*. 3#*" $.*. #*$ 3*%$ .*"- 3*.-

$"$3 ). $"# "3 "*. 3$*" $-*" #*$- 3*-$ .*-3 3*)+$"$% -# $". "% "*. 3%*. $+*- #*$+ 3*.$ .*%3 3*++

$"$. -. $3# ". "*. 3*# "$*. #*$+ 3*) .*.- 3*--

$"$) +# $%# ") 3 3*- "3*. #*$) 3*% )*$$ %*$3

$"$- +. $.# "+ 3 %+*+ "+*. #*$- 3*) .*-$ 3*+-

$"$+ # $)# 3# 3 .-*" 3"*# #*$- 3*-) .*+" 3*%

$""# $## $+# 3% 3*. )+* %#*. #*$- 3*)+ .*) %*+$

$""$ $#. $# 3) 3*. -%*$ %%*#

$""" $$# "## 3+ 3*. ++*% ."*#

$""% $"# "$. %" 3*. $$ -#*#

$$



?earin=s o< t9e out;ut s9a<t are arran=e5 as t9e <ie5 an5 <loatin=

su;;orts lo8ate5 in 6earin= 9ousin=s ,ta6le $3*"/* T9e <ie5 su;;ort 8an

ta>e u; 5ou6lesi5e5 aial loa5* hor t9at t9e inner an5 outer rin=s o< t9e

6earin= are <ie5 in 6ot9 aial 5ire8tions* T9e <loatin= su;;ort s9oul58o@;ensate 5e<or@ation o< t9e s9a<t* In t9is 8ase t9e inner rin= o< t9e

6earin= is <ie5 in 6ot9 5ire8tions* hor t9at 4e use 6oun5ary ;lates ,ta6les

$3*3 an5 $3*%/ or s;rin= rin=s ,ta6le $3*./* T9e outer rin= is le<t <ree*

Table 1).2Stan!a&! M "e&ie" 0ea&ing h#"ing" GOST 13-1.3;F9 mm

?ore 5ia@eter

D: @@ D$ d d $ ? B B$ # #$ " " $ h

+# $## M+ $3 $3. 3. %" $+# $$# $$3 .+ $

+. $#. M+ $3 $%# 3. %" $+. $$. $"#*. )3 $

# $$# M$# $3 $.# 3+ %" $. $". $3#*. )+ ""

$## $"# M$# $- $). %# %+ "$. $3. $3*. -" "%

$$# $3# M$# $- $+. %. %+ "3. $.. $.-*. +# ")

$"# $%. M$" $- "$# %+ %+ ")# $-. $-*. " 3"

$". $.# M$" $- ""# %+ %+ "-# $+# $++ + 3%

$3# $.. M$" $- "". .# .% "+# $+. $#*. + 3%$%# $). M$" "" "3. ." .+ ". $. $*. $#" 3.

$.# $+# M$" "" ".. .. )% 3$. "$# "$. $$# %#

$)# $# M$" "" ")# )# )% 3$. ""# "3# $"# %#

$-# "## M$" "" "+# )3 )) 33. "3# "%# $". %#

$+# "$# M$" "" "# )+ -. 3.. "%# ".# $3# %#

$# ""# M$) "" ". -# +" 3)# ".# ")# $3. %#

"## "3# M$) "" 3## -. +" 3). ")# "-# $%# %#

"$. ".# M$) "" 3". +. # 3+. "+. ""*. $.# %.

"". ")# M$) ") 3%# # . %$# ". 3#-*. $)# %+

$"#



Table1).) )#n!a&, +*ate GOST 15B35K>F9 mm

Desi=nation D " ? d d 2 c D> d ) d 1 l l 1

S8re4

,„’

--+-#/

Pin

,„’

3$"+-#/

-#$#)"3 3"

.

):) %:. $:#

"%***"+

2) % $+ $" 2)×$) %m+×$"

-#$#)". 3) $# "+***3"

-#$#)"- %# $# 3"***3)

-#$#)" %. $" 3)***%#

-#$#)3$ .# $) %#***%.

-#$#)33 .) $) %.***.#

-#$#)3. )3

)

"#

:# .:. $:)

.#***..

2+ . "" $) 2+×"# .m+×$)-#$#)3- )- "# ..***)#-#$#)3 -$ ". )#***).

-#$#)%$ -. ". ).***-#

-#$#)%3 +. "+ -#***-.

Ta6le $3*%

)#n!a&, +*ate ith t# "%&e" an! &etaining +*ate9 mm

$"$



D# D " D1 c l $ l " S8re4 d × l hro@ 3. to %# .#

)

"#

#:. "# "% 2+×"#a6ove %# to %. .. "#<ro@ %. to .# )# ".

<ro@ .# to )# -#+

3#

3# 3. ^$"×3#<ro@ )# to -# +# 3.

<ro@ -# to +# #$#

%#

<ro@ +# to # $$# %.

<ro@ # to $## $"#

$"

.#

3) %" ^$)×3)<ro@ $## to $$# $". ..

<ro@ $$# to $"# $%# )#

<ro@ $"# to $3# $.# ).

Table 1)./S+&ing "na+ &ing" an! g&##'e" $#& them Q 135-;>F9 mm

S9a<t

5ia@eter d

Grooves Rin=s

d $ B s b l

3. 33*#

$* $*-

%*

)*#

%# 3-*..*.

%. %"*.

.# %-*#

"*" "*#)*#

.. ."*#

)# .-*# )*.). )"*#

"*+ "*.

-*#-# )-*#

-. -"*#+*#

+# -)*.

$3*%* Desi=n t9e 5ru@ or s;ro8>ets o< t9e 8onveyer*

Dia@eter o< t9e 5ru@ ,s;ro8>et/ is =iven in t9e s;e8i<i8ation <or

t9e 8ourse ;roe8t*

$""



T9e 5ru@ ,s;ro8>ets/ s9oul5 6e @ounte5 on t9e out;ut s9a<t 6y

5istan8e $## or "## @@ relative to su;;orts*

T9ere eist 8ast 5ru@s an5 4el5e5 5ru@s* kel5e5 5ru@s are use5

@ore <reuently*hor 5eter@ination siBes o< t9e 8onveyer s;ro8>et it is ne8essary to

89oose a ;ull 89ain ,ta6le $3*)/*

Di@ensions o< t9e ;ull 89ain s;ro8>et are 5eter@ine5 in t9e

<ollo4in= 4ay7

a55en5u@ 8ir8le 5ia@eter Da Dz#*".j D$z)

@@g

5e5en5u@ 8ir8le 5ia@eter D - D D$g

4e6 t9i8>ness b#*j B 6us9g

49ere D is t9e no@inal ;it89 8ir8le 5ia@eter o< t9e s;ro8>et ,loo>

t9rou=9 t9e s;e8i<i8ation <or t9e 8ourse ;roe8t//g D$ is t9e 5ia@eter o<

t9e rollerg Bbush is t9e 6us9 4i5t9*

Possi6le 8onstru8tions o< 4el5e5 5ru@s are =iven in hi=*$3*"* T9e

ri@ an5 5is>s o< t9e 5ru@ are @a5e o< steel s9eet o< t9i8>ness + @@*

Ri6s o< t9e 5ru@ are ;ro5u8e5 <ro@ t9e stri; o< 4i5t9 %# @@ an5

t9i8>ness ) @@*

$"3



hi=* $3*"* kel5e5 5ru@s

$3*.* Desi=n t9e 4el5e5 <ra@e*

kel5e5 <ra@es are use5 <or @ountin= asse@6ly units* T9ey

s9oul5 8orres;on5 to 8ertain reuire@ents o< a88ura8y to ;rovi5enee5e5 relative 5is;osition o< asse@6ly units* ?esi5es: t9e 4el5e5 <ra@e

s9oul5 9ave 9i=9 ri=i5ity*

Table 1).0 Stan!a&! +** %hain" GOST < K 1F9 mm

t B 6us9 B ! ! $ d d $ D$ l l $$## 3"

3) . % $% "$3# )% 3.

$## 3+ 3) -# 3+

$". %% .# - - "# 3# %% $## .%

kel5e5 <ra@es are o6taine5 as a result o< 4el5in= steel rollin=

ele@ents su89 as 89annel 6ars: an=le , #/ 6ars: stri;s: s9eets an5 ot9ers*

C9annel 6ars are use5 @ore <reuently*

T9e 9ei=9t o< t9e 89annel 6ar is 5eter@ine5 as

" … #*$j #ma3:

49ere #ma3 is t9e @ai@u@ len=t9 o< t9e @e89ani8al 5rive*

O6taine5 value o< H s9oul5 6e roun5e5 o<< to t9e =reater si5e

a88or5in= to stan5ar5 series =iven in ta6le $3*-*In or5er to si@;li<y <iation o< asse@6ly units to t9e <ra@e

89annel 6ars are @ounte5 4it9 outsi5e <lan=es* hor ali=nin= t9e 6ase

sur<a8e <or t9e 6olt 9ea5 4e use s>e4 ;lates ,ta6le$3*+/*

I< asse@6ly units o< t9e @e89ani8al 5rive are lo8ate5 at 5i<<erent

levels 4e @ay use 8onstru8tions o< <ra@es =iven in hi=*$3*3: aJe*

$"%



Table 1).4 Channe*" GOST -5;B F9 mm

Nu@6er o<

89annel

Di@ensions: @@

h b s t

$% $%# .+ %* +*#

$) $)# )% .*# +*%

$+ $+# -# .*$ +*-

"#a "## +# .*" *#

""a ""# +- .*% *.

"%a "%# . .*) $#*-

"- "-# . ) $#*.

3# 3## $## )*. $$

33 33# $#. - $$*-Table 1).5

Stan!a&! "e +*ate" GOST 1> K BF

S>e4 ;lates ;ara@eters: @@

?olt

5ia@eter d $ " $ " B

$" $

3

.*- ) 3#

$) $

-

.*- ) 3#

$+ $

)*" - %#

"# "

"

)*" - %#

"" "

%

)*" - %#

"% "

)

)*+ .#

$".



hi=*$3*3* Alternatives o< <ra@es: 49en asse@6ly units are lo8ate5 at

5i<<erent levels*

Durin= o;eration o< t9e 6elt 5rive t9e 6elt stret89es* In or5er to

;rovi5e tension o< t9e 6elt at t9e reuire5 level 6elt tension a5usters are

use5* Possi6le 8onstru8tions o< 6elt tension a5usters are =iven inhi= $3*%: a% b an5 ta6le $3**

a b

$")



hi=*$3*%* Constru8tions o< 6elt tension a5usters*

Table1).6S*e!ge" $#& e*e%t&i% m#t#&

Ty;e

Di@ensions: @@

M a s s o < s e t : > =

S 8 r e 4 s < o r e n = i n e @ o u n t i n

=

a a$ B$ B" A $ d $ d " h$ h" h3 l

3 $) 3+ 3-# %%# %$# 2$" $" $. %% 3) %" 3:+ 2$#×3.

% $+ %. %3# .%# %-# 2$" $% $+ .. %. .# .:3 2$"×%#

. ". ). .-# )-# )"# 2$) $+ "" )- .. -" $":. 2$)×..

$"-



15. SHOP DRA(INGS O/ SPEED REDUCER ELEMENTS

A88or5in= to t9e s;e8i<i8ation <or t9e 8ourse ;a;er it is ne8essary to

@a>e t4o s9o; 5ra4in=s su89 as t9e s9o; 5ra4in= o< t9e s;ee5 re5u8er out;ut s9a<t an5 t9e s9o; 5ra4in= o< t9e toot9e5 49eel*

Sh#+ !&aing #$ the #t+t "ha$t

T9e s9o; 5ra4in= is 8arrie5 out to s8ale $7$ or $7"* hirst o< all: it is

ne8essary to ;lot t9e out;ut s9a<t a88or5in= to t9e 5i@ensions o<

asse@6ly 5ra4in=* T9e s9a<t @ust 6e 5ra4n in t9e ;osition o< installin=

on a @a89ine: i*e* t9e ais o< t9e s9a<t s9oul5 6e ;arallel to t9e @ain

ins8ri;tion* Transition <ro@ one installin= 5ia@eter to t9e ot9er is

8arrie5 out 6y @eans o< <illets or =rooves* hillets are use5 49en t9e

installin= sur<a8e is not =roun5* S9a<t ;ortions 49ere 6earin=s are

installe5 s9oul5 6e =roun5* As a s;a8e reuire5 <or =rin5in= 49eel

=rooves are use5* Possi6le alternatives o< =rooves are s9o4n in ta6le

$%*$* Di@ensions o< =rooves are =iven in ta6le $%*$* In t9e s9o;

5ra4in= =rooves s9oul5 6e re;resente5 to t9e in8rease5 s8ale se;arately*

Table 1*.1G&##'e" $#& a g&in!ing hee* in "ha$t" an! thei& !imen"i#n"9 mm

d b d $ $

Over $# to .# 3 d #*. #*$ #*.

Over .# to $## . d J #*. $*) #*.

Over $## + d $*# "*# $*#

T9e net ste; is 5i@ensionin= t9e 5ra4in=* T9e nu@6er o<

5i@ensions s9oul5 6e @ini@al 6ut enou=9 to ;ro5u8e t9e s9a<t*

C9a@<ers an5 =rooves 4i5t9 8annot 6e in8lu5e5 to t9e total 5i@ensions

89ain*

T9ere eist t9ree @et9o5s o< 5i@ensionin= 5ra4in=s7

$"+



89ain @et9o5 t9at ;rovi5es t9e a88ura8y o< 5is;osition o<

every <ollo4in= ele@ent relative to t9e ;revious* In t9is 8ase t9e

a88ura8y relative to 8ertain 6ase is 5e8rease5g

8oor5inate @et9o5 a88or5in= to 49i89 5i@ensionin= o< a5ra4in= is 8arrie5 out 4it9 res;e8t to 6ase ?g

8o@6ine5 @et9o5 t9at 8onsists o< t9e 89ain an5 8oor5inate

@et9o5s*

hor t9e s9o; 5ra4in= t9e re8o@@en5e5 @et9o5 is 8o@6ine5

@et9o5* Di@ensionin= in t9e aial 5ire8tion is 8arrie5 out un5er an

ele@ent 5ra4in=*

As it is >no4n 5i@ension @ust 6e 9el5 6et4een t4o li@its* T9e

5i<<eren8e o< t9ese li@its is 8alle5 toleran8e* Toleran8e li@its o<

relatively lo4 a88ura8y 5i@ensions are not @ar>e5 on a 5ra4in=* In t9is

8ase it is ne8essary to @a>e t9e <ollo4in= ins8ri;tion7

F Dimensional toleances holes "1*% sha-ts h1*% othe elementsIT$%

"±

@medium accuacC class*

T9e nature o< ele@ents 8onne8tions is 8alle5 a <it* hits @ay ;rovi5e

8learan8e or inter<eren8e* T9ere eist also transition <its t9at @ay 9ave

eit9er 8learan8e or inter<eren8e* hits are @ar>e5 6y a letter o< Ro@an

al;9a6et* Letters ah 8orres;on5s to 8learan8es: Nsn transition <its: p+ inter<eren8e* A nu@eral near a letter s9o4s t9e uality =ra5e* T9ere

eist $ uality =ra5es* hor @e89ani8al en=ineerin= t9e @ost ty;i8al are

uality =ra5es . t9rou=9 $"* “uality =ra5es ) t9rou=9 + re<er to 8riti8al

;arts an5 units*

Ea@;le o< t9e s9a<t 5ra4in= hi=* $%*$: ea@;le o< t9e =ears

8onstru8tion hi=* $%*"$%*%*

/it" #$ main e*ement"

$* Strai=9t s;ur =ear on t9e s9a<t

-)

" p g

"* Heli8al s;ur =ear an5 4or@ =ear on t9e s9a<t

-

)

"

g

3* ?evel =ear on t9e s9a<t

-

)

"

s g

%* Cou;lin= an5 =ear lo8ate5 on a 8antilever ;ortion o< t9e s9a<t -

)

"

k g

$"



.* Pulleys or s;ro8>ets

-

)

"

h g

)* Co@@er8ial seals h$$g

-* Inner rin= o< a 6earin= k )g+* Outer rin= o< a 6earin= " -g

* T9e 4i5t9 o< a >eyseat in t9e s9a<t P g

$#*T9e 4i5t9 o< a >eyseat in t9e 9ole o< a 9u6 O ! *

Durin= treat@ent o< t9e s9a<t 6esi5es errors o< linear 5i@ensions

errors o< =eo@etri8al s9a;es an5 errors o< sur<a8es 5is;osition arise*

Possi6le errors o< =eo@etri8al s9a;es are non8ylin5ri8al sur<a8es:

nonroun5in=: non<lattin=*hor s9a<t ;ortions an5 =ear 9oles toleran8es o< 8ylin5ri8al sur<a8e

s9oul5 6e ta>en into a88ount* Si=n ” @ar>s toleran8e o< 8ylin5ri8al

sur<a8e* T9e @a=nitu5e o< t9is toleran8e is 5eter@ine5 as #*3qt q$#3:

49ere t is 5ia@etri8al toleran8e ran=e in @i8ro@eters ,ta6le $%*"/*

O6taine5 value o< t9e toleran8e s9oul5 6e roun5e5 o<< a88or5in= to t9e

<ollo4in= stan5ar5 series7 #*##%: #*##.: #*##): #*##+: #*#$: #*#$": #*#$):

#*#"*

Table 1*.2T#*e&an%e &ange" in mi%&#mete&"

Di@ensions in

@@

“uality =ra5es

3 % . ) - + $# $$ $" $3 $%

Over 3 to . "*. % . + $" $+ 3# %+ -. $"# $+# 3##

Over ) to $# "*. % ) $. "" 3) .+ # $.# ""# 3)#

Over $# to $+ 3 . + $$ $+ "- %3 -# $$# $+# "-# %3#

Over $+ to 3# % ) $3 "$ 33 ." +% $3# "$# 33# ."#

Over 3# to .# % - $$ $) ". 3 )" $## $)# ".# 3# )"#Over .# to +# . + $3 $ 3# %) -% $"# $# 3## %)# -%#

Over +# to $"# ) $# $. "" 3. .% +- $%# ""# 3.# .%# +-#

Over $"# to

$+#+ $" $+ ". %# )3 $## $)# ".# %## )3# $###

Over $+# to

".#$# $% "# " %) -" $$. $+. "# %)# -"# $$.#

Possi6le errors o< sur<a8e 5is;ositions are non;er;en5i8ularity

relative to a 6ase: @isali=n@ent: nonsy@@etry: non;arallelis@*

$3#



hor s9a<ts it is ne8essary to use total toleran8es t9at ta>e into a88ount

toleran8e o< s9a;e an5 toleran8e o< sur<a8e 5is;osition7 ra5ial runout

t9at allo4s <or nonroun5in= an5 @isali=n@ent an5 en5;lay t9at ta>es

into a88ount non<lattin= an5 non;er;en5i8ularity*T9e @a=nitu5e o< ra5ial runout 5e;en5s u;on t9e ;eri;9eral

s;ee5 an5 is 5eter@ine5 a88or5in= to ta6le $%*3*

T9e @a=nitu5es o< en5 ;lay @ay 6e <oun5 a88or5in= to ta6le

$%*%*

Table 1*.) T#*e&an%e" #$ &a!ia* &n #t #$ "ha$t +#&ti#n" $#& $itting t##the! hee*"9

+**e,"9 %#+*ing"

Peri;9eral s;ee5 o< ele@ents

@ounte5 on a s9a<t: @se8 " ") )$# $#

Toleran8e o< ra5ial run out "*#jtj$#3 $*%jtj$#3 $*#jtj$#3 #*-jtj$#3

Table 1*.*T#*e&an%e" #$ en! +*a, #$ gea&ing"9 h0"9 #$ t##the! hee*" an! "ha$t

"h#*!e&"

De=ree o<

a88ura8y

hor =earin= at d $## @@:

an5 at <a8e 4i5t9 o<

hor toot9e5 49eel 9u6 an5 s9a<t

s9oul5er at 6ore 5ia@eter ,s9a<t

5ia@eter o</

.. ..$$# .. ..+# +#

) #*#$- #*## #*#" #*#3 #*#%

- #*#"$ #*#$$ #*#" #*#3 #*#%

+ #*#") #*#$% #*#3 #*#% #*#.

#*#3% #*#$+ #*#3 #*#% #*#.

As a 6ase t9e s9a<t ais o< rotation is use5 <or sur<a8es 49ere

6earin=s are installe5* In or5er to eli@inate @isali=n@ents o< ele@entst9at are installe5 on t9e s9a<t 4e 4ill use as a 6ase o< all ot9er s9a<t

sur<a8es: t9e sur<a8es 49ere 6earin=s are lo8ate5*

Possi6le errors o< a >eyseat are non;arallelis@ an5 nonsy@@etry*

Parallelis@ toleran8e is @ar>e5 as an5 is eual to #*)jt ksj$#3: 49ere t ks

is >eyseat 4i5t9 toleran8e ran=e in @i8ro@eres ,ta6le $%*"/* Sy@@etry

toleran8e is @ar>e5 as ÷ an5 is %jt ksj$#3*

T9e net ste; is @ar>in= sur<a8es rou=9ness*

$3$



Sur<a8e rou=9ness @ay 6e evaluate5 6y avera=e 5eviation o< ;ro<ile

a or 9ei=9t o< ;ro<ile irre=ularities + 6y ten ;oints* Mar>in= sur<a8e

rou=9ness 6y a is @ore ;re<era6le* T9e @a=nitu5e o< sur<a8e rou=9ness

5e;en5s u;on t9e sur<a8e treat@ent an5 t9e uality =ra5e*

Main "&$a%e" &#ghne""

s9a<t ;ortions <or installin= 6earin=s #*+g

s9a<t ;ortions <or installin= =ears: 9al<8ou;lin=s: s;ro8>ets:

;ulleys7

i< d .. @@ #*+: i< .. d $"# $*)g

s9oul5er <a8e en5 <or 6earin=s <iation $*)g

s9oul5er <a8e en5 <or <iation o< =ears: s;ro8>ets: ;ulleys: 9al<

8ou;lin=s 3*"g

s9a<t ;otion <or installin= seals #*"g

4or>in= sur<a8es o< a >eyseat @a5e in t9e s9a<t $*)g

9oles o< =ears t9at are installe5 on t9e s9a<t

i< d .. @@ #*+g

i< ..@@ d $"#@@ $*)g

=ear <a8e en5 t9at is <ie5 6y t9e s9a<t s9oul5er or t9e <a8e en5 o<

ot9er ele@ent 3*"g

<ree =ear <a8e en5 )*3g toot9 ;ro<ile

<or )t9 5e=ree o< a88ura8y #*%g

<or -t9 5e=ree o< a88ura8y #*+g

<or +t9 5e=ree o< a88ura8y $*)g

<or t9 5e=ree o< a88ura8y 3*"g

4or>in= sur<a8es o< a >eyseat @a5e in t9e 9u6 3*"*

$3"



h i = *

$ % * $ *

i n =

h i = *

$ % * " *

= e a r

$33



h i = *

$ % * 3 *

= e a r

$3%



h i = *

$ % * % *

= e a r

$3.



1<. DESIGN O/ A PARTS LIST

A88or5in= to GOST "*$#+) a Parts List is @a5e in t9e <or@ o<

ta6les on se;arate A% ;a;ers <or every asse@6ly unit*T9e Parts List 8onsists o< t9e <ollo4in= su6;arts7

$* Do8u@entation

"* Asse@6ly Units

3* Ele@ents

%* Stan5ar5 Ele@ents

.* Materials

T9e na@e o< every su6;art 9as to 6e 4ritten in t9e <or@ o< t9e

un5erline5 title in t9e 6o FDes8ri;tion* It is re8o@@en5e5 to re@ain

$3 <ree lines <or ;ossi6le a55itional re8or5s*

T9e su6;art FDo8u@entation in8lu5es t9e @ain set o< 5esi=n

5o8u@entation: <or ea@;le FAsse@6ly Dra4in=: FE;lanatory Note:

et8*

T9e su6;art FAsse@6ly Units in8lu5es asse@6ly units: 49i89 are

;arts o< t9e @ain ite@* hor ea@;le: FS;ee5 re5u8er: Fkel5e5 hra@e:

F?elt Tension A5uster: FDru@ S9a<t: Fkor@ Gear: FDee; Sti8>:

et8*

T9e su6;art FEle@ents in8lu5es nonstan5ar5 ele@ents* hor ea@;le: F Gear: FIn;ut S9a<t: FCa;: F?earin= Housin=: FDriven

Pulley: FDrivin= S;ro8>et: et8* It is re8o@@en5e5 to list t9e@

al;9a6eti8ally*

T9e su6;art FStan5ar5 Ele@ents in8lu5es state an5 in5ustry

stan5ar5 ite@s* Stan5ar5 ele@ents are 5ivi5e5 into =rou;s: e*=* <astenin=

ele@ents: 6earin=s: et8* an5 are liste5 al;9a6eti8ally*

T9e su6;art FMaterials in8lu5es @aterials use5 in t9e ite@: <or

49i89 t9e ;arts list is @a5e* hor ea@;le: FIn5ustrial Oil: Fkire: et8*Parts list 6oes to 6e <ille5 in as <ollo4in=7

$* T9e FPa;er SiBe 6o 8ontains t9e ;a;er siBe o< t9e ite@

5ra4in= ,A$: A": A3: A%/* I< t9ere is no 5ra4in= <or an ite@

t9is 6o is <ille5 in 6y kD ,kit9out Dra4in=/* hor su6;arts

FStan5ar5 Ele@ents an5 FMaterials t9is 6o s9oul5 not 6e

<ille5 in*

"* T9e FArea 6o is not <ille5 in <or 8ourse ;roe8ts*

$3)



3* T9e FIte@ No* 6o 8ontains 8onse8utive nu@6er o< t9e

5esi=ne5 ite@ 8o@;onent ;arts* hor su6;art FDo8u@entation

t9is 6o s9oul5 not 6e <ille5 in*

%* T9e FPart Nu@6er 6o 8ontains 5esi=nation o< 5o8u@ents:asse@6ly units an5 ele@ents* hor su6;arts FStan5ar5 Ele@ents

an5 FMaterials t9is 6o s9oul5 not 6e <ille5 in*

.* T9e FDes8ri;tion 6o 8ontains

a/ T9e na@e o< a 5o8u@ent <or su6;art FDo8u@entation ,<or

ea@;le: Asse@6ly Dra4in=: E;lanatory Note: et8*/

6/ T9e na@e o< an ite@ a88or5in= to t9e @ain ins8ri;tion on

t9e 5ra4in= <or su6;arts FAsse@6ly Units an5 FEle@ents

,<or ea@;le ?evel Gear: Out;ut S9a<t: et8*/

8/ T9e na@e an5 5esi=nation o< an ite@ a88or5in= to state or

in5ustrial stan5ar5 <or su6;arts FStan5ar5 Ele@ents an5

FMaterials ,<or ea@;le: ?olt M$"-#*.+ GOST --+-#*/

)* T9e F“uantity 6o 8ontains t9e nu@6er o< asse@6ly units:

ele@ents an5 stan5ar5 ele@ents <or one ite@

-* T9e FNotes 6o 8ontains a55itional in<or@ation a6out

ele@ents: 5o8u@ents: @aterials*

At t9e 6otto@ o< t9e Parts List t9e @ain <ra@e is @a5e si@ilar as <or

5ra4in=s*De"ignati#n #$ !e"ign !#%mentati#n

Desi=nation o< 5esi=n 5o8u@entation 8onsists o< t9e <ollo4in= ;arts7

NAU $"* #3*#%*##. AA:

49ere

NAU is t9e institution 8o5e

$ is t9e nu@6er o< tas>

" is t9e nu@6er o< variant

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t9e @e89ani8al 5rive/ is @ar>e5 6y nu@6er $ on t9e @e89ani8al 5rive

5ra4in= t9e s;ee5 re5u8er s9oul5 6e 5esi=nate5 as <ollo4in=

NAU $"*#$*##*### AD*

#% is t9e 8onse8utive nu@6er o< asse@6ly units 49i89 are a ;art o< t9e

@ain asse@6ly units* hor ea@;le: i< t9e 4or@ =ear ,asse@6ly unit o<

t9e s;ee5 re5u8er/ is @ar>e5 6y nu@6er % on t9e s;ee5 re5u8er 5ra4in=

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s9oul5 6e 5esi=nate5 as <ollo4in= NAU $"*##*##*##-*

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<ollo4in=

NAU $"*#3*#%*##*

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@ar>e5 6y AD: e;lanatory note 6y EN: ;arts list 6y PL* T9e

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8ontain t9e 5o8u@ent 8o5e*

T9e ea@;le o< t9e Parts List <or t9e @e89ani8al 5rive is =iven in

hi=*$.*$*

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+* šc\£ Š* ‰* XW Z\WX]Z_V Y]ZX\\ Š* ‰* šc\£: ‘* —*

—X£Z\* (*7 ˜W1 Z\: $-* $.$ W*

* Ma89ine Ele@ents* Ter@ ;a;er 5esi=nin=7 @anual A*S*KryB9anovs>yi:

A*O*Kornien>o: O*!*?as9ta an5 ot9ers* K*7 NAU: "#$$$"% ;*

$%$



CONTENTS

Intro5u8tion***

*$* Kine@ati8 an5 <or8e analysis o< a @e89ani8al 5rive ***

"* Analysis o< allo4a6le stresses **

3* Analysis o< t9e strai=9t s;ur =ears <or stren=t9 ****

%* Analysis o< t9e 9eli8al s;ur =ears <or stren=t9 *

.* Analysis o< t9e 6evel =ear <or stren=t9 ***

**

)* Analysis o< t9e 4or@ =earin=**

**

-* Analysis o< t9e <lat 6elt 5rive ***

+* Analysis o< t9e 89ain 5rive ***

* Analysis o< s9a<ts**

$#* S9a<t analysis <or stren=t9 **

$$* Analysis o< t9e rollin= 8onta8t 6earin=s *

$"* Desi=nin= t9e =ear s;ee5

re5u8er****

$3* Desi=nin= t9e @e89ani8al 5rive *

$%* S9o; 5ra4in=s o< s;ee5 re5u8er ele@ents***

3

%

$%

"-

"

3"

%3

%-

.3

)-

-

+3

$#

)

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$"

.$3

corse project guide

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