Лекции - Расчёт и конструирование машин непрерывного транспорта

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/$H+8A 45

!/&'8&8-(H'O&% '/A8C D/&8?= /-'89/'=@+8>8 -,)9,:H-/++% -=D+/@*+8U 9/&=

-/+'/C( D/ )8;898>8H A8+-*N:+=0 -/>, ;8 ;8A/D/++H %A=0 ;:8-/)='O&% -=9=A/++%

A8+-*N:/ /?8 C=-=$O+=A/ ;,&$% ;:8;(&A/++% +=9= G,NU 9/&= -/+'/C(.

3 -

-'89/'=@+* D-/C(-/++% +/&=;+8>8 -/+'/C(, S8 ' :/+ &; 8:'(N'O&% ;:8-/)='O&%

?*D;8&*:*)+O8 +/ A8+-*N:, /?8 +/ 8A:*98 -&'/+8-$*+=0 -/>8-=0 />:*>/'/0.

8 :*C=9, D-/C(-/++% /-'89/'=@+, -/>= :8D),$%H'O +/ (&':8U ;*:*:=-/+8U ,

?*D(;=++8U ),U, ;8 D/&8?, D-/C(-/++% , '=;( (&':8H - +/ 9*0/+,@+, '/ *$*A':8++,

(*$*A':=@+,).

&'/++,9 @/&89 <=:8A* ;8<=:*++% D+/08)%'O ?,$O< ; :8&', , A89;/A'+, *$*A':8++,

-/>=, S8 :8?$%'O 8;*:/G,U ;8 9=''N-89( D-/C(-/++H -/+'/C( +/ &':,@G, 7 ,+'*>:(-/++H

;8A/D/+O 9/&= D/ @/&89. := -=9,:, :8D;8),$*+8>8 +/-/+'/C*++% +/ &':,@G, -/>8-/

:8$,A8;8:/ &;:=79/N '=&A +/ UU -/+'/C( , ;*:*)/N 8;8:+=9 *$*9*+'/9, +/;:(>( , ;:(C+/

)*.8:9/G,% %A=0 .,A&(N'O&% )/'@=A89, S8 :8?='O -,);8-,)+, D9,+= - *$*A':=@+,7 &=&'*9,.

8 U0+O89( :8D9,:( -&'/+8-$HN'O&% 9/&/ -/+'/C( +/ )8-C=+, 1 9 ( 989*+' -=9,:(.

)+8@/&+8 D/ )8; 898>8H ;:='=&+('8>8 )8 &':,@A= , 8?*:'/HS=9(&% D/:/D89 D +*H

?*D ;:8&$=D/++% ?/:/?/+/ /?8 :8$,A/ -=D+/@/N'O&% <-=)A,&'O &':,@A= , 9/&8-/

;:8)(A'=-+8&'O A8+-*N:/.

/7?,$O<* D/&'8&(-/++% 9/H'O )/'@=A= ':O80 '=;,-: ,+)(AG,7+,, 9/>+,'8(;:(>, '/

'*+D89*':,@+,.

 ,+)(AG,7+89( )/'@=A( ;,) ),NH &=$= -/>= -/+'/C(, ;:= )*.8:9(-/++, 8;8:+8>8

*$*9*+'/, ;*:*9,S/N'O&%, &;8$(@*+=7 D 8&'/++,9 &'/$*-=7 &*:)*@+=A S8)8 )-80 -0,)+=0

- *$*A':=@+( &=&'*9( A8'(<8A. +/&$,)8A GO8>8 D9,+HH'O&% ,+)(A'=-+=7 8;,: A8'(<8A ,

&=$/ '8A ( - &=&'*9,, :*>($O8-/+/ -=9,:H-/$O+=9 ;:=$/)89.

,% 9/>+,(;:(>=0 )/'@=A,- ,D .*:89/>+,'+=0 9/'*:,/$,- D/&+8-/+* +/ '89(, S8

+/;:(>/ ;:= U0+O89( &'=&A( /?8 :8D'%>( &;:=@=+%N D9,+( 9/>+,'+8U ;:8+=A+8&',, S8

-=A$=A/N D9,+( *$*A':=@+8>8 8;, :( &=&'*9=.

/7?,$O< ;8<=:*+, '*+D89*':,@+, )/'@=A=, %-$%H'O &8?8H *$*9*+'= D )(C* '8+A8>8

):8'(, ;8A$/)*+8>8 ( -=>$%), ;*'*$O. /A, )/'@=A= +/A$*HH'O +/ ;:=79/H@( &=$( -/>=

-/+'/C( )*'/$, '/A=9 @=+89, S8 ;:= U0 )*.8:9/G,U &'=&A( H'O&% /?8 :8D'%>(H'O&%

;:%98$,+,7+, ),$%+A= ;*'*$O )/'@=A/, (+/&$,)8A @8>8 D9,+HN'O&% D/>/$O+=7 *$*A':=@+=7

8;,: &=&'*9=. $% D?,$O<*++% D9,+ ;/:/9*':,- &=&'*9= D-=@/7+8 -A$H@/H'O - *$*A':=@+=7

$/+GH> ;,)&=$H-/@.

17. () 

/),7+,&'O - -$/&'=-,&'O 9/<=+= -=A8+(-/'= D/)/+, .(+AG,U, D?*:,>/H@= &-8U

*A&;$(/'/G,7+, ;8A/D+=A= - ;*:*)?/@*+=0 9*C/0 ;:8'%>89 +*8?0,)+8>8 ;:89,CA( @/&(.

/),7+,&'O 8?'NA'/ A,$OA,&+8 8G,+HN'O&% D/ )8;898>8H &=&'*9= ;8A/D+=A,-, S8

-=?=:/H'O&% D (:/0(-/++%9 8&8?$=-8&'*7 8?'NA'/, :*C=9,- , (98- 78>8 *A&;$( /'/G,U ,

+/&$,)A,- -,)98-.

/),7+,&'O - A89;$*A&+/ -$/&'=-,&'O

, S8 ( D/$*C+8&', -,) ;:=D+/@*++% 8?'NA'/ 7 (98-

78>8 *A&;$(/'/G,U 98C* -A$H@/'= (9/$H+8A 46): ?*D-,)98-+,&'O, )8->8-,@+,&'O,

:*98+'8D)/'+,&'O, D?*:*>,)+,&'O - 8A:*98 /?8 &;8$(@*++% G=0 -$/&'=-8&'*7 %A 8?'NA'/ -

G,$89(, '/A , 78>8 @/&'=+ (.

,)98-/ - G* ;8),%, S8 ;8$%>/N - ;8:(<*++, ;:/G*D)/'+8&', -=:8?(.

:/G*D)/'+,&'O - &'/+ 9/<=+=, ;:= %A89( -8+/ &;:898C+/ -=A8+(-/'= D/)/+, .(+AG,U,

D?*:,>/H@= D+/@*++% D/)/+=0 ;/:/9*':,- ( 9*C/0, -&'/+8-$*+=0 +8:9/'=-+8-'*0+,@+8H

)8A(9*+'/G,NH.

=;8-, -,)98-=:

- ;8$89A= )*'/$*7;

- '*+),'+, :(7+/G,U;

- ;8-D(@,&'O;

- ;$/&'=@+, )*.8:9/G,U;

- -'89/ 9/'*:,/$,-;

- D+8<(-/++% :8?8@=0 ;8-*:08+O )*'/$*7: /?:/D=-+*, >,):8/?:/D,-+*,

;+*-98/?:/D,-+*, *:8D,7+*.

8:8D,% - ;:8G*& :(7+/G,U 9/'*:,/$,- (+/&$,)8A 0,9,@+8>8 /?8 *$*A':80,9,@+8>8 -;$=-(

D8-+,<+O8>8 &*:*)8-=S/.

+   

/;'8-/ -,)98-/ -,)?(-/N'O&% @*:*D:

- ;*:*-=S*++% @=++8>8 +/-/+'/C*++% +*&(@8U &;:898C+8&', 8?'NA'/;

- (+/&$,)8A +/%-+8&', ;:=08-/+=0 )*.*A',- -=>8'8-$*++%;

- ( :*D($O'/', ;89=$8A :8D:/0(+A( , A8+&':(H-/++%;

- ( :*D($O'/', ;8:(<*++% ;:/-=$ *A&;$(/'/G,U.

8&'(;8-/ -,)98-/ +/&'(;/N ;:= ;8-+89( -=A8:=&'/++, :*&(:&( 8?'NA'/ -+/&$,)8A

;:=:8)+8>8 &'/:,++% /?8 D+8<(-/++% 9/'*:,/$( 8?'NA'/.

)=+=@+, ;8A/D+=A= +/),7+8&', 9/<=+

8+= 0/:/A'*:=D(H'O %A(&O 8)+( 78>8 -$/&'=-,&'O: ?*D-,)98-+,&'O, )8->8-,@+,&'O,

:*98+'8;:=>,)+,&'O /?8 D?*:*C*++,&'O.

*D-,)98-+,&'O - -$/&'=-,&'O 9/<=+= ?*D(;=++8 D?*:,>/'= ;:/G*D)/'+,&'O ;:8'%>89

D/)/+8>8 @/&( /?8 +/:8?,'A=.

8->8-,@+,&'O

- -$/&'=-,&'O 9/<=+= )8->8&':8A8-8 D?*:,>/'= ;:/G*D)/'+,&'O )8

>:/+=@+8>8 &'/+/ ;:= -&'/+8-$*+,7 &=&'*9, '*0+,@+8>8 8?&$(>8-(-/++% , :*98+',-.

!?*:*C*+,&'O - -$/&'=-,&'O 8?'NA'/ D?*:,>/'= D+/@*++% ;8A/D+=A,- ?*D-,)98-+8&',,

)8->8-,@+8&', , :*98+' 8D)/'+8&', ;,&$% D?*:*C*++% , ':/+&;8:'(-/++%.

/$H+8A 46

8+&':(AG,7+, -,)98-= - 8?(98-$*+, ;89=$A/9=, S8 ;:=;(&A/H'O&% ;:= ;:8*A'(-/++,,

D/+=C*++%9 D/;/&,- ':=-A8&',, ;89=$A/9= - :8D:8?G, ;:=+G=;8-=0 &0*9 , A8+&':(AG,7

(&':8U-.

=:8?+=@, -,)98-= - -=D=-/H'O&% ;8:(<*++%9= '*0+8$8>,U -=>8'8-$*++%,

D/&'8&(-/++%9 +*A8+&':(AG,7+=0 9/'*:,/$,- /?8 +*)8&'/'+,9 A8+':8$*9 %A8&', - ;:8G*&,

-=:8?+=G'-/.

8+&':(AG,7+, , -=:8?+=@, -,)98-=, %A ;:/-=$8, -=%-$%H'O&% - ;8@/'A8-=7 ;*:,8)

*A&;$(/'/G,U. 8+= 98C( 'O ?('= -=%-$*+, '/A8C ( ;:8G*&, )8-,)+=0 ,&;=',- ( D/-8)&OA=0

(98-/0.

A&;$(/'/G,7+, -,)98-= N &$,)&'-89 ;8:(<*+O (98- :8?8'=, +/ %A, :8D:/08-/+/

9/<=+/, +*)8':=9/++% 8?>8-8:*+=0 ( '*0+,@+,7 )8A(9*+'/G,U ;:/-=$ *A&;$(/'/G,U, +=DA8H

A-/$,.,A/G,U 8?&$(>8-(H@8>8 ;*:&8+/$(, ;:=:8)+O8>8 &'/:,++%, D+8<(-/++% 7 ,+<=0

;:=@=+. A&;$(/'/G,7+, -,)98-= -=%-$%H'O&% +* ',$OA= - ;8@/'A8-=7 ;*:,8) *A&;$(/'/G,U,

/$* 7 ( +/&'(;+=7 @/& :8?8'=.

8 0/:/A'*:, ;:8%-( (&, -,)98-= ;8),$%H'O +/ :/;'8-, , ;8&'(;8-,. AS8 - %A8&',

(D/>/$O+*+8>8 ;/:/9*':/, S8 0/:/A'*:=D(N ;:/G*D)/'+,&'O 9/<=+=, 98C$=-8 -=?:/'=

-*A'8: «y» ('=&A, :8?8'(, D+8& '/ ,+<*), '8 :/;'8-, , ;8&'(;8-, -,)98-= -=D+/@/H'O&%

<-=)A,&'H D9,+= (D/>/$O+*+8>8 ;/:/9*':/.

8 ;8&'(;8-=0 -,)98- &'/-$%'O&% '/A,, )$% %A=0 <-=)A,&'O D9,+= (D/>/$O+*+8>8 ;/:/9*':/

9/N &A,+@*++( -*$=@=+( (A:=-/ 2 9/$H+8A 47). 8&'(;8-, -,)98-= 9/<=+= N &$,)&'-89

+*8?8:8'+=0 D9,+ UU -$/&'=-8&'*7, -=A$=A/+=0 &'/:,++%9, D+8&89, +/A8;=@*++%9

(<A8)C*+O , D9,+8H ;/:/9*':,- :8?8@8> 8 ;:8G*&(. /;'8-, -,)98-= (A:=-/ 1)

0/:/A'*:=D(H'O&% :,DA8H, &':=?A8;8),?+8H D9,+8H (D/>/$O+*+8>8 ;/:/9*':/ ;,) -;$=-89

8)+8>8 /?8 )*A,$OA80 8?(:*+O, -=A$=A/+=0 -+(':,<+,9= )*.*A'/9=, ;8:(<*++%9= :*C=9,-

:8?8'= /?8 ;89=$A/9= 8?&$(>8-(H@8>8 ;*:&8+/$(. !-=@/7+8 ;8%-, :/;'8-=0 -,)98-

;*:*)(H'O ;:=08-/+, )*.*A'= /?8 D9,+= -$/&'=-8&'*7 *$*9*+',-, S8 +* D/-C)= -)/N'O&%

D/(-/C='= , -=%-='=.

!/$*C+,&'O -=0,)+=0 ;/:/9*':,- -,) @/&( , -,)98-=

/$H+8A 47

1 – :/;'8-/ -,)98-/, 2- ;8&'(;8-/ -,)98-/

:= ;8&'(;8-=0 -,)98-/0 0/:/A'*:=&'=A= 9/<=+= D9,+HH'O&% - @/&(, , 8'C*

;:=+G=;8-8 98C$=-8 D/ )8;898>8H &;*G,/$O+8U &=&'*9= A8+':8$H /?8 &;*G,/$O+=0 ,&;=',-

;:8>+8D(-/'= 989*+' +/&'/++% -,)98-= , -C='= D/08),-, S8 D/?*D;*@(H'O D?*:,>/++%

;:/G*D)/'+8&', 9/<=+=.

8&'(;8-, -,)98-=, S8 98C$=-8 ;:8>+8D(-/'=, +/D=-/H'O ;:8>+8D8-/+=9=. AS8

;8D+/@='= @/& ;8@/'A( :8D-='A( -,)98-= t

, / @/& D/-*:<*++% t

'8 œt=t

-t

+/D=-/N'O&%

@/&89 *A&;8D=G,U -,)98-=.

=&'*9/ A8+' :8$ H &'/+/ 9/N -=D+/@*+( <-=)A8),H t

S8 D/$*C='O -,) &0*9= 7 (&':8H

&=&'*9= A8+':8$H , <-=)A8&', D9,+= A8+':8$O8-/+8>8 ;/:/9*':/. := œt>t

, -,)98-/

:/0(N'O&% ;:8>+8D8-/+8, ;:= œt<t

- -,)98-/ +*;:8>+8D(N' O&% , UU 98C+/ -,)+*&'= )8

A/'*>8:,U :/;'8-=0.

8 &'(;*+, -;$=-( +/ ;:/G*D)/'+,&'O 9/<=+= (&, -,)98-= 98C+/ :8D),$='= +/ ;8-+, ,

@/&'A8-,.

:= ;8-+=0 -,)98-/0 -,)?(-/N'O&% -':/'/ ;:/G*D)/'+8&', 9/<=+=. := @/&'A8-=0

-,)98-/0 &;:898C+,&'O 9/<=+= )8 -=A8+/++% &-8U0 .(+AG,7 D?*:,>/N'O&%, ;:8'* ;:= GO89(

D+=C(N'O&% *.*A'=-+,&'O U0 -=A8+/++%.

$% ;:=-8),-, -&'/+8-$*+=0 ( 9/<=+/0, S8 -=A8+(H'O -,);8-,)/$O+, .(+AG,U, -,)98-=

),$%'O&% +/ +*?*D;*@+, , ?*D;*@+,.

,$OA,&+, ;8A/D+=A= +/),7+8&', 9/<=+

,$OA,&+, ;8A/D+=A= +/),7+8&', - G* 98C$=-8&', -=D+/@*+=0 ;8),7, 8?(98-$*+,

-$/&'=-8&'%9= '*0+,@+=0 8?'NA',-.

8C$=-,&'O +/?(-/N A,$OA,&+=7 (9/'*9/'=@+=7) D9,&' , &'/N 9,:8H +/),7+8&',, A8$=

98C$=-,&'O ;:8%-( %A8U&O ;8),U 8G,+HN'O&% %A=9-+*?()O @=&$89, &',7A=9 ;:=

A,$OA/:/D8-89( ;8-'8:*++, )*%A8>8 A89;$*A&( (98-.

8C$=-,&'O ;8),U '*8:*'=@+8 -=D+/@/N'O&% D/$*C+,&'H:

NnP

/lim



= , (17.1)

)* n - A,$OA,&'O ;8),7;

N - A,$OA,&'O ,&;=',-.

*/$O+* D+/@*++% 98C$=-8&', 8?9*C*+8, 8&A,$OA= -8+8 9/N &*+& ',$OA= ;:= +*D9,++89(

A89;$*A&, (98- ;:8'%>89 %A D/->8)+8 -*$=A8>8 @/&(. ,$O< ;:=7+%'+=9 N -=D+/@*++%

98C$=-8&', %A )*%A8>8 8?'NA'=-+8>8 :8D9,:(, ;8?$=D( %A8>8 >:(; (H'O&% @/&'8'= P

=n/N

)8&'/'+O8 -*$=A=0 &*:,7 ,&;=',-.

!/A8+ :8D;8),$( -=;/)A8-8>8 :8D9,:( N UU (+,-*:&/$O+8H -*:8%'+8&'+8H

0/:/A'*:=&'=A8H.

!/A8+89 :8D;8),$( 98C$=-8&'*7 -=;/)A8-8>8 :8D9,:( +/D=-/N'O&% -&%A* &;,--,)+8<*++%,

S8 -&'/+8-$HN D-'%D8A 9,C 98C$=-=9= D+/@*++%9= -=;/)A8-8>8 :8D9,:( , -,);8-,)+=9=

U9 98C$=-8&'%9=.

!/A8+ :8D;8),$( 9/N :,D+, .8:9=: :%) :8D;8),$(, ,+'*>:/$O+/ .(+A G ,% :8D;8),$( ,

)=.*:*+G,/$O+8U .(+AG,U :8D;8),$(.

+'*>:/$O+8H . (+AG,NH :8D;8),$( 98C$=-8&'*7 -=;/)A8-8>8 :8D9,:(  +/D=-/N'O&%

.(+AG,% F(x), -=D+/@/N'O&% )$% A8C+8>8 D+/@*++% /:>(9*+'( 0 98C$=-,&'O ;8),U X<x

&A$/)/N'O&% - '89(, S8 -=;/)A8-=7 :8D9,: X ;:=79* D+/@*++% 9*+<* 0, '8?'8

F(x)=P(X<x). +'*>:/$O+/ .(+AG,% F (x), %A (&%A/ 98C$=-,&'O, N ?*D:8D9,:+8H -*$=@=+8H.

*89*':=@*&A= G* 8D+/@/N, S8 F (x) N 98C$=-,&'O '8>8, S8 -=;/)A8-=7 :8D9,: 

;:=D+/@*++%, S8 D8?:/C(N'O&% +/ @=&$8-,7 8&, '8@A8H, :8D'/<8-/+8U $*-,N '8@A= 0.

8;8-+*++% ,+'*>:/$O+8U .(+AG,U :8D;8),$( -=;/)A8-8>8 :8D9,:(  -=D+/@/N 98C$=-,&'O

;:8'=$*C+8U ;8),U X>x , +/D=-/N'O&% .(+AG,% )()( xFxP = , S8 -=D+/@/N )$% A8C+8>8

D+/@*++% /:>( 9*+'( 0 98C$=-,&'O ;8),U X>x, S8 &A$/)/N - '89(, S8 ':/;$%N'O&% :8D9,: 

;:=79* D+/@*++%, ?,$O<* 0, '8?'8:

)(1)()()( xFF ==>= . (17.2)

*89*':=@*&A, G* 8D+/@/N, S8 N 98C$=-,&'O '8>8, S8 -=;/)A8-=7 :8D9,:  ;:=79*

D+/@*++%, S8 D8?:/C(N'O&% +/ @=&$8-,7 8&, '8@A8H, :8D'/<8-/+8U &;:/-/ -,) '8@A= 0.

8),% X<x , X>x (+/;:=A$/), -,)98-/ , -,)&('+,&'O -,)98-=) - -=;/)A8-, :8D),$O+,

;:8'=$*C+, ;8),U, S8 ('-8:%'O ;8-+( >:(;(, )8:,-+HN 8)=+=G,, '8?'8:

1)()(

xPxF . (17.3)

* :,-+%++% )8D-8$%'='= -=D+/@='= 8)+( D G=0 .(+AG,7 ;8 -,)898U ,+<=7.

+'*>:/$O+/ .(+AG,% :8D;8),$( , UU )8;8-+*++% - '*8:,U +/),7+8&', 0/:/A'*:=D(H'O

:,D+89/+,'+, -=;/)A8-, :8D9,:=:

/& :8?8'= 8?'NA'/ )8 -,)98-=, :*&(:& , '*:9,+ &$(C?= 8?'NA'/, @/& -,)+8-$*++%

;:/G*D)/'+8&', 8?'NA'/, '*:9,+ D?*:,>/++% 8?'NA'/.

8C$=-,&'O ($(@*++% -=;/)A8-8>8 :8D9,:(  - ,+'*:-/$ , b )8:,-+HN D?,$O<*++H

,+'*>:/$O+( .(+AG,H +/ GO89( ,+'*:-/$,:

)()()( aFbFbX



(17.4)

8C$=-,&'O -,)98-= 8?'NA'/ - .(+AG,% F(t), S8 -=D+/@/N )$% A8C+8>8 D+/@*++% @/&( t

98C$=-,&'O ;8),U t

, S8 &A$/)/N - '89(, S8 @/&  :8?8'= 8?'NA'/ )8 -,)98-= ;:=79*

D+/@*++%, 9*+<* t, '8?'8:

)()( tTPtF

% .(+AG,% -=D+/@/N 98C$=-,&'O -=+=A+*++% -,)98-= 8?'NA'/ - ,+'*:-/$, @/&( t.

8C$=-,&'O ?*D-,)98-+8U :8?8'= 8?'NA'/ - .(+AG,% (t), S8 -=D+/@/N )$% A8C+8>8

D+/@*++% @/&( t 98C$=-,&'O ;8),U T>t, S8 &A$/)/N - '89(, S8 @/&  :8?8'= 8?'NA'/ )8

-,)98-= ;:=79* D+/@*++%, ?,$O<* t, '8?'8:

)(1)()()( tFtFtTPtP ==>= . (17.5)

% .(+AG,% -=D+/@/N @/& ?*D-,)98-+8U :8?8'= 8?'NA'/, S8 -=D+/@/N 98C$=-,&'O

?*D-,)98-+8U :8?8'= 8?'NA'/ - ,+'*:-/$, @/&( t.

=.*:*+G,/$O+/ .(+AG,% :8D;8),$( 98C$=-8&'*7 -=;/)A8-8>8 :8D9,: ( N ;*:<8H

;80,)+8H -,) ,+'*>:/$O+8U -,) ,+'*>:/$O+8U .(+AG,U :8D;8),$(

xdF

xFxxF



)()()(

lim)(









. (17.6)

:8)=.,:=+G(-/- -=:/C*++%

1)()(

xPxF , 8)*:C=98:

xdP

xdF

)()(

)( ==

. (17.7)

*89*':=@+8 )=.*:*+G,/$O+/ .(+AG,% %A ;80,)+/ ,+'*>:/$O+8U .(+AG,U -=D+/@/N '/+>*+&

:8>( 9,C -,&&H /?&G=& , )8'=@+8U )8 ,+'*>:/$O+8U .(+AG,U - )/+,7 UU '8@G,. 8D9,:+,&'O

)=.*:*+G,/$O+8U .(+AG,U 8?*:+*+/ :8D9,:+8&', -=;/)A8-8>8 :8D9,:(.

/&'8'/ ;8%-= ;8),7

N 98C$=-,&'H U0+O8>8 ;:8%-= - 8)=+=GH @/&( . =.*:*+G,/$O+/

.(+AG,% -=D+/@/N 98C$=-,&'O ;8%-= ;8),7 - 8)=+=GH @/&( , S8 98C* ?('= ,+'*>:8-/+/ %A

@/&'8'/ ;8%-= ;8),7, +/;:=A$/), @/&'8'/ -,)98- 8?'NA',-, @/&'8'/ -,)+8-$*++%

;:/G*D)/'+8&', 8?'NA',-.

/&'8'/ -,)98- (S,$O+,&'O :8D;8),$( @/&( :8?8'= 8?'NA'/ )8 -,)98-=) ;8 &'/'=&'=@+,7

,+.8:9/G,U -=D+/@/N'O&% %A -,)+8<*++% @=&$/ 8?'NA',-, S8 -,)98-=$= - 8)=+=GH @/&(, )8

@=&$/ 8?'NA',- +/ ;8@/'A( ,&;='( ;8 .8:9($,:

tnttn











)0(

)(

)0(

)()(

)(

, (17.8)

)* œt - ,+'*:-/$ @/&( -,) t )8 t+œt; n(œt) - @=&$8 8?'NA',-, S8 -,)98-=$= - ,+'*:-/$, @/&( œt;

n(t) - @=&$8 8?'NA',-, S8 -,)98-=$= D/ @/& t; N(0)=N(t)+n(z) - @=&$8 8?'NA',- +/ ;8@/'A(

,&;='(.

:/.,A )=.*:*+G,/$O+8U .(+AG,U :8D;8),$( 98C$=-8&'*7 -=;/)A8-8>8 :8D9,:(,

;8?()8-/+=7 ;8 &'/'=&'=@+,7 ,+.8:9/G,U, +/D=-/H'O >=&'8>:/987.

$% UU ;8?()8-= :8D?=-/H'O -*&O ),/;/D8+ 98C$=-=0 D+/@*+O ?*D(;=++8>8 -=;/)A8-8>8

:8D9,:( +/ ,+'*:-/$= œt D-=@/7+8 :,-+8U )8-C=+= , )$% A8C+8>8 ,+'*:-/$( -=D+/@/H'O ;8

8&'/+,7 .8:9($, D+/@*++% f

(z), S8 -,)A$/)/H'O ;8 8&, 8:)=+/'.  :*D($O'/', ('-8:HN'O&%

+/?$=C*+* (% -$*++% A:=-8U )=.*:*+G,/$O+8U .(+AG,U ( -=), &0,)@/&'8U $,+,U. 8C$=-,&'O

($(@*++% ?*D(;=++8>8 -=;/)A8-8>8 :8D9,:( - D/)/+=7 ,+'*:-/$ (,b), -=:/C*+* @*:*D

)=.*:,+G,7+, .(+AG,U, -=D+/@/N'O&% ,+'*>:(-/++% ( 9*C/0 -,)  )8 b.



<<====



bxaPaFbFxFxdFdxxf )( )()()()()(

, (17.9)

'8?'8 98C$=-,&'O ($(@*++% ?*D(;=++8>8 -=;/)A8-8>8 :8D9,:(  - D/)/+=7 ,+'*:-/$ (,b)

)8:,-+HN -=D+/@*+89( ,+'*>:/$( -,) )=.*:*+G,7+8U .(+AG,U - 9*C/0 -,)  )8 b.

*89*':=@+8 98C$=-,&'O ($(@*++% ?*D(;=++8>8 -=;/)A8-8>8 :8D9,:(  - ,+'*:-/$ (,b)

)8:,-+HN ;$8S, A:=-8$,+,7+8U ':/;*G,U, 8?9*C*+=9 -,&&H /?&G=&, >:/.,A89 )=.. .(+AG,U

f(x) , ;:%9=9= x=a, x=b.

* ) 

:= &':(A'(:+89( /+/$,D, 8;*:(H'O ,D D/)/+=9= *$*9*+'/9= , D-'%DA/9= 9,C +=9=, S8

-8$8),H'O D/)/+=9= 0/:/A'*:=&'=A/9= +/),7+8&',. ;8@/'A( &A$/)/H'O &':(A'(:+(

&0*9( +/),7+8&', A8+-*N:/, ;:= GO89( -:/08-(H'O 78>8 *$*9*+'= , ;:=@=++8-$8>,@+,

D-'%DA= 9,C +=9=.

8D;8),$ ?()O-%A8U 9*0/+,@+8U &=&'*9= 98C$=-8 +/ )*A,$OA80 :,-+%0, , '89( ;:=

.,A&8-/+89( :,-+, :8D;8),$= -,)89=7 ( $8>,G, ;:=+G=; )-8U&'8&', $8>,@+=0 D-'%DA,-

-=%-$%N'O&% +* ',$OA= - &':(A'( :, &=&'*9= (98C$=-,&'O )-80 :,D+89/+,'+=0 &0*9

-9=A/++% *$*9*+',- ; 8&$,)8-+8>8 , :,-+8?,C+8>8), /$* , ( -+(':,<+,7 &':(A'(:, -,)98-

8)+8>8 *$*9*+'/.

':,@A8-=7 A8+-*N: ;8),$%H'O +/: / - :8$,A88;8:=, &':,@A(, ;:=-,) , '.).; ? - :8$,A88;8:(

- +/ :/9( , :8$,A=; - - :8$,A= - +/ 8?*@/7A(, (S,$O+*++%, ;,)<=;+=A=, 8&, , '.).

 9*0/+,@+=0 &=&'*9/0 98C$=-8 )-/ '=;= -,)98- *$*9*+',-: A,+*9/'=@+=7 , &=$8-=7.

:= GO89( '87 &/9=7 *$*9*+' 98C$=-8 :8D>$%)/'= &;8$(@*+=9 ( D9,&', +/),7+8&',

;8&$,)8-+8 , ;/:/$*$O+8. := -=D+/@*++, +/),7+8&', '/A 8U &=&'*9= -/:'8 -:/08-(-/'=

)-8U&',&'O -,)98- UU *$*9*+',-.

':(A'(:+, 9*'8)= /+/$,D( +/),7+8&', D/&+8-/+, +/ 98C$=-8&', (%-$*++% D9,+HHS=0&%

;8-,$O+8 :8D;8),$*+=0 ( @/&( , ;:8&'8:, ;:8G*&,- )=&A:*'+=9 ;8:(@ :,-+8-/C+=0 &'/+,-

:= GO89( ;8$%>/H'O, S8 ;:8'%>89 -=D+/@*+=0 ;:89,CA,- @/&( &':(A'(:+, D-'%DA= -

&=&'*9, D/$=</H'O&% +*D9,++=9= , 98C$=-8 D+*-/C='= -D/N9+=9 -;$=-89 +/),7+8&',

8)+8>8 *$*9*+'/ +/ ,+<=7. /;:=A$/), D/-C)= 98C+/ D )8&'/'+O8H ;,)&'/-8H

;:=;(&'='=, S8 :8? 8'/ ;:=-8)( , :8$,A88;8: +*D/$*C+/ - D9,&', +/),7+8&',.

:= +/7;:8&',<89( &':(A'(:+89( /+/$,D, &=&'*9( ;8)/H'O ( -=), >:/./, -*:<=+/9= %A8>8

N *$*9*+'= &=&'*9=, / :*?:/9= - D-'%DA= 9,C +=9=. &+8-+=9 D'N)+/++%9 *$*9*+',- ( >:/.,

;:=7+%'8 --/C/'= ;8&$,)8-+* D'N)+/++% 1,2,3...m´. := '/A89( D'N)+/++, (;8&$,)8-+/

(&'/+8-A/ A8+-*N:,- ( '*0+8$8>,@+89( $/+GH>(), 98C$=-,&'O ?*D-,)98-+8U :8? 8'=  (&O8>8

$/+GH>/ *$*9*+',- ) 8:,-+HN '-8:8-, 98C$=-8&'*7 

, 

,...,

(&,0 *$*9*+',-

/$H+8A 48. 8&$,)8-+* D'N)+/++% ':/+&;8:'+=0 9/<=+

:=A$/): :8D)=-=98&% %A :8D:/08-(H'O ;8A/D+=A= +/),7+8&', &':,@A8-8>8 A8+-*N:/ ;:=

-=),$*++, - +O89( ':O80 8&+8-+=0 *$*9*+',-: &':,@A= :8$, A88;8: , ;:=-8) (. :=;(&'=98,

S8 -,)98-/ ?()O %A8>8 D *$*9*+',- ;:=D-8)='O )8 -,)98-= -&O8>8 A 8+-*N:/.  GO89(

-=;/)A( *$*9*+'= &;8$(@*+, ;8&$,)8-+8 - D9,&', +/),7+8&',.

/),7+,&'O A8+-*N:/ -=D+/@/H'O %A:









(17.10)

AS8

021

... 



====



, '*







(17.11)

,D (17.11) -=;$=-/N, S8 +/),7+,&'O A8+-*N:/ 9*+<* +/),7+8&', A8C+8>8 D 78>8 *$*9*+',-.

AS8 .(+AG,U +/),7+8&', (&,0 *$*9*+',- 8)+/A8-, , 9/H'O -=):





= (17.12)

/1= - ,+'*+&=-+,&'O -,)98-; dttT





)( - &*:*)+,7 +/:8?,'8A )8 -,)98-= i->8

*$*9*+'/ A8+-*N:/, '8 +/),7+,&'O (&O8>8 A8+-*N:/ '/A8C ;,);8:%)A8-(N'O&%

*A&;8+*+G,/$O+89( D/A8+( (17.12) , -,);8-,)+8 )8 :,-+ %++% (17.10) 9/N -=):



i







+++

)

...(

, (17.13)





++++=



...

321

'C* &*:*)+,7 +/:8?,'8A )8 -,)98-= A8+-*N:/ )8:,-+HN:













+++











00201

...

/?8 ;:=





=== ...

9/N98













. (17.14)

 '/?$=G, +/)/+, :*D($O'/'= )8&$,)C*++% ;:8'%>89 -8&O9= :8A,- +/),7+8&', &':,@A8-8>8

A8+-*N:/ D?/>/@(-/$O+8U ./?:=A=. 8-C=+/ A8+-*N:/ 256 9, <=:=+/ &':,@A= 2000 99, :,>

+/0=$( 10‚. 8&$,)C (-/$=&% '/A, -(D$=: &':,@A/, ;:=-,)+/ &'/+G,%, :8$,A88;8:= -/+'/C+8U

, +*8):(C*+8U >,$A=.  :*D($O'/', 8;:/GH-/++% )/+=0 8':=9/+, D+/@*++% @/&(

?*D-,)98-+8U :8?8'= t

, ;:8&'8U- t

;

(D8$ /&

-&'/+8-$*++%,

/:8?,

'8A +/

-,)98-

(, @

+'*+&=-+,&

'O -,)98-

':,@A/

:=-,)+/

&'/+G,%

8$,A88;8:=

12,7

7,6

7,8

663,3

673,3

494,2

0,0015

0,00148

0,00203

/),7+,&'O A8+-*N:,- $,+,U, S8 &A$/)/N D )*A,$OA80 ;8&$,)8-+8 ;:/GHH@=0 A8+-*N:,-,

;,):/08-(H'O ;8 '=9 C* .8:9($/9. AS8 (%-='= A8+-*N:+( $,+,H &A$/)/+( D @8'=:O80

;8&$,)8-+8 ;:/GHH@=0 A8+-*N:,- D 8)+/A8-8H +/),7+,&'H, '8 ;:= 

=132 @, &*:*)+%

+/),7+,&'O )8 -,)98-= -&,NU $,+,U



0¢

= 

=132/4=33 @..

*:,)A8 -=A8:=&'8-(H'O $,+,U D :,-+8?,C+=9 /?8 D A89?,+8-/+=9 D'N)+/++%9

(;8&$,)8-+8-:,-+8?,C+=9 , +/-;/A=) A8+-*N:,-:

/$H+8A 49. 8&$,)8-+8-:,-+8?,C+/ &0*9/ ':/+&;8:'+=0 9/<=+

 :,-+8?,C+=0 &0*9/0 ?*D :*D*:-(-/++% -,)98-/ 8)+8>8 A8+-*N:/ +* 8?8-'%DA8-8 -*)* )8

-,)98-= -&,NU &=&'*9=. ,)9,++8H :=&8H ':/+&;8:'+=0 &=&'*9 &A$/)/N'O&%, ( '89(, S8

;:8)(A'=-+,&'O &=&'*9=,

( %A,7 +* ;*:*)?/@*+* :*D*:-(-/++% A8+-*N:,- ;:= -,)98-/0

8A:*9=0 (&'/+8-8A D9*+<(N'O&%. =&'*9= GO8>8 '=;( +/D=-/H'O

?/>/'8.(+AG,8+/$O+=9=, '8?'8 ;:/GHH@=9= - :,D+89/+,'+=0 &'/+/0 ,D :,D+8H

*.*A'=-+,&'H. 8&$,)C*++% +/),7+8&', ?/>/'8.(+AG,8+/$O+=0 &=&'*9 ;8-'%D/+8 D

-=D+/@*++%9 A:='*:,U- *.*A'=-+8&', U0+O8U :8?8'=.  %A8&', '/A8>8 A:='*:,H 98C+/

;:=7+%'= ':/+&;8:'(H@( &;:898C+,&'O

,V , '*0+8$8>,@+8U &0*9= (9/'*9/'=@+=7 8;=&

UU ;:8)(A'=-+8&',):

[]



=

ipi

QTtPVM

)(

, (17.15)

- 98C$=-* @=&$8 ;:/G*D)/'+=0 &'/+,- &=&'*9=;

- 98C$=-,&'O ;*:*?(-/++% &=&'*9= - ,-9( ;:/G*D)/'+89( &'/+,;

T - ;$/+8-/+=7 @/& :8?8'=;

- '*0+,@+/ ;:8)(A'=-+,&'O &=&'*9= - ,-9( ;:/G*D)/'+89( &'/+,.

.*A'=-+,&'O :8?8'= A8+-*N:+=0 $,+,7:

)$% &0*9= D :,-+8?,C+=9= +*D/$*C+=9= -/+'/C8;8'8A/9=

[]



i

TVM

, (17.16)

)$% &0*9= D 8?'N)+/++%9 -/+'/C8;8'8A,-:

[

]

[

]

3221121

)( QQQQV



+++= , (17.17)

i

T ,

T - &*:*)+,7 @/& -,)+8-$*++% , &*:*)+% +/:8?,'A= )8 -,)98-= i-7 A8+-*N:+8U $,+,U

-,);8-,)+8;

321

,,  - 98C$=-,&'O ':O80 ;:/G*D)/'+=0 &'/+,- &0*9= D 8?'N)+/++%9

-/+'/C8;8'8A,-.

 &=&'*9, D :,-+8? ,C+=9= -/+'/C8;8'8A/9= , :*-*:&=-+=9 ;*:*-/+'/C(-/$O+=9 (&':8N9

1 '*0+,@+/ ;:8)(A'=-+,&'O QQQ ==

. *-*:&=-+=7 ;*:*-/+'/C( -/$O+=7 (&':,7

;8),$%N A8C+= 7 A89;$*A& +/ )-, @/&'=+=, ;:=@89( A 8+-*N:=, S8 D/;='(H'O&% ;,&$%

;*:*-/+'/C(-/$O+8>8 (&':8H, 9/H'O @/&'A8-=7 :*D*:- '*0 +,@+8U ;:8)(A'=-+8&',, S8

D/?*D;*@(N ;:=789 )*%A8>8 )8)/'A8-8>8 8?&%>( -/+'/C( ;:= -,)98-, :,-+8?,C+8U ),$%+A=

A8+-*N:+8U &=&'*9=. AS8 -,)+8<*++% 



/ )$% -&,0 @8'=:O80 ),$%+8A, +/ %A,

;*:*-/+'/C(-/$O+=7 (&':,7 ;8),$%N )-, A8+-*N:+, $,+ ,U, )8:,-+HN 0,15, / :*D*:-

;:8)(A'=-+8&', D?,:+=0 $,+,7 &A$/)/N 0,5Q. :/+&;8:'(H@/ &;:898C+,&'O &=&'*9= -

;8:,-+%++, D )-89/ +*D/$*C+=9= A8+-*N:+=9= $,+,%9= D?,$O<(N'O&% - 5,5 :/D (.

8D)=-=98&% A8+-*N:+, &=&'*9= D ;8-+=9 :*D*:-(-/++%9 ;8 ;:8)(A'=-+8&',.

:8)(A'=-+,&'O '/A8U &=&'*9= +* D9,+HN'O&% ;:= ?()O-%A=0 ;:/G*D)/'+=0 &'/+/0.

/7;:8&',<=7 ;:=A$/) D 8)+8H :8?8@8U 7 8)+8H :*D*:-+8H $,+,NH (9/$H+8A 3).

 ?()O-%A=7 989*+' @/&( ;:/GHN ',$OA= 8)+/ D )-80 $,+,7 (1-2 /?8 3-4). 8C$=-,&'O

-,)98-= -&,NU &=&'*9= )8:, -+HN ' -8:8-, 98C$=-8&'*7 -,)98-= 8?80 $,+,7. 89(

98C$=-,&'O ?*D-,)98-+8U :8?8'= &=&'*9=:

)1)(1(1

  = ,

, - 98C$=-8&', ?*D-,)98-+8U :8?8'= 8&+8-+8U , :*D *:-+8U $, +,7.

+<=9 '=;89 :*D*:-8-/+8U A8+-*N:+8U &=&'*9= N &=&'*9/ D :8?8@8U , :*D *:-+8U $,+,7 ,

&;8$(@*+=0 ( )*A,$OA80 9,&G%0 :*-*:&=-+=9= ;*:*-/+'/C(-/$O+=9= (&':8%9=. AS8

;*:*-/+'/C(-/$O+, (&':8U /?&8$H'+8 +/),7+,, '8 /+/$,D8-/+/ &=&'*9/ ;*:*'-8:HN'O&% -

&=&'*9( D ;8&$,)8-+8-:,-+8?,C+=9 D'N)+/++%9 ),$%+8A A8+-*N:+=0 $,+,7, 98C$=-,&'O

?*D-,)98-+8U :8?8'= %A8U )8:,-+HN ;:= +/%-+8&', 8)+8>8 ;*:*-/+'/C(-/$O+8>8 ;(+A'(:

[

]

[

]

)1)(1(1)1)(1(1

4321

  = . (17.18)

/:/9*':=@+/ +/),7+,&'O A8+-*N:,-

$% ;/:/9*':=@+8U +/),7+8&', 0/:/A'*:+8 )8&$,)C*++% .,D=@+=0 ;:8G*&,-, S8

;:=D-8)%'O )8 -,)98-, '8?'8 )8&$,)C*++% -=;/)A,-, A8$= ;/:/9*':= &=&'*9= -=08)%'O D/

;/:/9*':= S8 ;:=;(&A/H'O&%: D+8&, :(7+/G,%, &'/:,++% , '.).

&+8-( )8&$,)C*+O ;/:/9*':=@+8U +/),7+8&', &A$/)/H'O ':= -D/N98D/$*C+, ;8$8C*++%:

1) (98-= *A&;$(/'/G,U A8+&':(AG,7 , U0+N ;8-8)C*++% - ;:8G*&, *A&;$(/'/G,U N

-=;/)A8-=9= ;:8G*&/9=;

2) 8'8'8C+HH'O +/),7+,&'O , 98C$=-,&'O ;*:*?(-/++% ;/:/9*':,- A8+&':(AG,U - )*%A,7

;:=;(&'=9,7 8?$/&',, -,)98-( ,+'*;:*'(H'O %A -=0,) ,D G,NU 8?$/&',;

3) -=0,) A8+&':(AG,U D $/)( N &$,)&'-89 +/A8;=@*++% (<A8)C*+O, D/$=<A8-=0

)*.8:9/G,7, S8, )8&%>+(-<= -=D+/@*+8>8 :8D9,:(, ;8@=+/H'O ;*:*<A8)C/'= UU

+8:9/$O+,7 *A&;$(/'/G,U.

8D:/0(+8A 9*0/+,@+8U A8+&':(AG,U +*D/$*C+8 -,) -=)( +/-/+'/C*+O &A$/)/N'O&% %A ;:=

)*'*:9,+,&'=@+89(, '/ A , ;:= -*:8>,)+8&'+89 ;,)08), D )-80 *'/;,-: ;*:*?(-/++%

-*:8>,)+8&'+=0 0/:/A'*:=&'=A ;8-8)C*++% A8+&':(AG,U ;8 D/)/+=9 -*:8>,)+8&'+=9

0/:/A'*:=&'=A/0 D8-+,<+,0 (98- , UU A8+&':(A'=-+=0 ;/:/9*':,- (D/)/@/ &'/'=@+8U

)=+/9,A=); -&'/+8-$*++% +*?*D;*@+=0 &'/+,- , 8?@=&$*++% 98C$=-8&', U0 -=+=A+*++%

(D/)/@/ '*8:,U +/),7+8&',).

*:<=7 *'/; &A$/)/N'O&% ( -=),$*++, &=&'*9= D +/-A8$=<+O8>8 &*:*)8-=S/,

-*:8>,)+8&'+89 8;=&, D8-+,<+,0 -;$=-,-, &0*9/'=D/G,U , .8:9/$,D/G,U &=&'*9= , D8-+,<+,0

-;$=-,- '/ -$/&+* :,<*++% D/)/@, &'/'=@+8U )=+/9,A=.

:(>=7 *'/; &A$/)/N'O&% ( -=?,:, ;:8&'8:( %A8&', 7 8?$/&', ;:=;(&'=9=0 D+/@*+O

;/:/9*':,- &=&'*9=, -=08)%@= D *A8+89,@+=0, '*0+8$8>,@+=0 , *A&;$(/'/G,7+=0 -=98>,

;*:*?(-/++% .(+AG,U +/),7+8&', 7 8&*:*)+*++% UU ;8 9+8C=+, -;$=-,- , &=&'*9.

8C$=-,&'O -,)98-= :8$,A88;8:= 98C+/ -=D+/@='= %A 98C$=-,&'O -=A=)( -=;/)A8-8>8

:8D9,:( /?8 -=;/)A8-8>8 ;:8G*&(, S8 0/:/A'*:=D(N &'/+ :8$,A88;8:=, D 8?$/&',

;:=;(&'=98U D9,+= UU &'/+(.

/;:=A$/), -,)98-/ :8$,A88;8:= &':,@A8-8>8 A8+-*N:/ 98C* ?('= 8?(98-$*+=7 N)=+=9

;,A8-=9 )=+/9,@+=9 +/-/+'/C*++%9 /?8 )*.8:9/G,NH, S8 ;*:*-=S(N ;:=;(&'=9,

D+/@*++% (:(7+/G,U -(D$/ D'N)+/++% :8$,A=- ;,)-,&+8U :8$,A88;8:= &':,@A8-8>8 A8+-*N:/

/?8 D:=- .('*:8-A= :8$,A/ ;:= ()/:, D+/@+8>8 <9/'A/ -/+'/C(, ;*:*-/+'/C*++%

/98:'=D/'8:/ ;,)-,&+8U :8$,A88;8:= D/-/+'/C(-/$O+8>8 (&':8H &':,@A8-8>8 A8+-*N:/).

:=A$/): := ':/+&;8:'(-/++, &A*$O+=0 ;(&A8-=0 ;8:,) D/&'8&8-(H'O &':,@A8-,

A8+-*N:= D ;,)-,&+=9= :8$,A88;8:/9=. *C=9 :8?8'= ;,)-,&+=0 :8$,A88;8: ( 9,&G%0

D/-/+'/C*++% )(C* -/CA=7. 8$89A/ :8$,A88;8:= - 9,&G, D/-/+'/C*++% ;:=D-8)='O )8

;:=;=+*++% A8+-*N:/, '8?'8 )8 ;:8&'8U-.

G,+=98 +/),7+,&'O :8?8'= '/A8U :8$,A88;8:=, D 8>$%)( +/ '*, S8 +/-/+'/C*++% N

&'/G,8+/:+=9 -=;/)A8-=9 ;:8G*&89.  %A8&', A:='*:,H ;:/G*D)/'+8>8 &'/+/ ;:=79*98