Лекции - Расчёт и конструирование машин непрерывного транспорта

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8*.,G,N+'  -=D+/@/H'O ( D/$*C+8&', -,) -,)+8&+8U <8:&'A8&', ” ;8-*:0+, -,)A:='8>8

C8$8?/ , >,):/-$,@+8>8 :/),(&/ R.

8:%)8A :8D:/0(+A( ;/:/9*':,- ;:= ':/+&;8:'(-/++, ;8 $8'A/0 , A/+/$/9

:*A89*+)(N'O&% '/A=7:

1) ;8 D/)/+89( 8?&%D, -/+'/C(, S8 ;*:*9,S/N'O&% V´ (9

/>) , A8* .,G ,N+' :8D;(<*++% -

+/&=;G, 

(

>1) -=D+/@/H'O :8D:/0(+A8-=7 8?'N9 V=V´/

;

2) ( -,);8-,)+8&', ;:=-*)*+=9= -=S* -A/D,-A/9= ;:=79/H'O A8+G*+':/G,H >,):8&(9,<,

S , D+/08)%'O ;:8)(A'=-+,&'O ;8 >,):8&(9,<, V

/>);

3) ;8',9 -=?=:/H'O <-=)A,&'O >,):8&(<, a, :,-+( /?8 )*A,$OA/ ?,$O<( A:='=@+8U;

4) ;:=7+%-<= .8:9( , &;,--,)+8<*++% :8D9,:,- -,)A:='8>8 C8$8?/, ;8 :8D9,:/0V

, a

-=D+/@/H'O >*89*':=@+, :8D9,:= 78>8 ;*:*'=+= , D+/08)%'O >,):/-$,@+=7 :/),(& R.

5) 8?:/-<= - D/$*C+8&', -,) 9,&G*-=0 (98- '87 /?8 ,+<=7 -=) ;8-*:0+, C8$8?/

;($O;8-8)/ 7 (&'/+8-=- )$% +O8>8 -,)+8&+( <8:&'A,&'O, ( D/$*C+8&', -,) D+/@*+O R , ”

D+/08)%'O A8*.,G,N+' #*D, ;

6) ;8 .8:9($, ,=a

/(

]R) -=D+/@/H'O +*8?0,)+=7 (0=$ C8$8?/ ,.

 ?/>/'O80 ;:/A'=@+=0 -=;/)A/0 (0=$ C8$8? / -=D+/@/N'O&% :*$ON.89 9,&G*-8&',. :=

+/)$=<A8-89( (0=$, )8G,$O+8 D/&'8&8-(-/'= C8$8?/ D ;,)-=S*+8H -,)+8&+8H <8:&'A,&'H,

/ - 8?*:+*+89( -=;/)A( D, D+=C*+8U.

16. !" # $ %. &

(+A*:/ %-$%H'O &8?8H &()=+=, S8 9/H'O (>8:, D/-/+'/C(-/$O+,, / +/&;8),

:8D-/+'/C(-/$O+, 8'-8:=. 8D-/+'/C(-/$O+, 8'-8:= ;*:*A:=-/H'O&% D/'-8:/9=.

(+A*:/ D/&'8&8-(H'O )$% ;:=789(, D?*:*C*++% , ;8)/@, +/ ':/+&;8:'+, D/&8?=

+/&=;+=0 -/+'/C,-.

:= +/%-+8&', ;:89,C+=0 N9+8&'*7 ( -=), ?(+A*:,- ( D/>/$O+ 89( $/+GHD,

':/+&;8:'+=0 , '*0+8$8>,@+=0 9/<=+ 8&'/++, ;:/GHH'O +*D/$*C+8 ,+<=7 -,) ):(>/, S8

)8D-8$%N -&'/+8-$H-/'= )$% +=0 +/7?,$O<* )8G,$O+, :*C=9=.

*:*&(-/++% -/+'/C( ;8 ?(+A*:, , -=',A/++% @*:*D 8'-8:= -,)?(-/H'O&% ;,) ),NH &=$=

-/>=.

./01 

(+A*:/ D/&'8&8-(H'O - (&'/+8-A/0 ':O80 '=;,-: S8 /A(9($HH'O, D:,-+%$O+=0 '/

'*0+8$8>,@+=0.

&'/+8-A=, S8 /A (9($HH'O, &$(C/'O )$% D?*:*C*++% +/&=;+=0 -/+'/C,- , ;8&'/@*+,

(&':8%9= )$% D/-/+'/C*++% , :8D-/+'/C*++% N9+8&'*7, (&':8%9= )$% -=9,:( 9/&= 7 ,+<=9=.

!:,-+%$O+, (&'/+8-A= N ;:89,C+=9= )$% '=9@/&8-8>8 D?*:*C*++% &=;(@=0 ;:89,C+=0

;:8)(A',- -=:8?+=G'-/ (+/;:=A$/), -,)&'87+, N9+8&', )$% .8:9(-/$O+8U D*9$,, S8

;:808$8)C(H'O N9+8&', , '.;.).

!/&'8&8-(H'O D/A:=', , -,)A:=', ;8-*:0+, ?(+A*:/. ,)A:=', ?(+A*:/ )*<*-<*

D/A:='=0, /$* U0 -=A8:=&'8-(H'O $=<* )$% -/+'/C,-, S8 +* ;&(H'O&% -,) -;$=-(

/'98&.*:+=0 8&/)A,- , +* ;:=D-8)%@=0 ;=$HA=, '8?'8 <A,)$=-=0 )$% D)8:8-'%

8?&$(>8-(H@8>8 ;*:&8+/$(.

 D/A:='=0 ?(+A*:/0 ,D A8+,@+=9 )/089 -,)&('+, ;8:8C+, D8+= ;:= D/;8-+*++,. 

?(+A*:/0 C* D ;$8&A=9= ;*:*A:=''%9= D/-C)= 9/H'O ;8:8C+, D8+=, 8&8?$=-8 ;:= ?,@+89(

:8D'/<(-/++, D/-/+'/C(-/$O+8>8 8'-8:(. 8:8C+, D8+= +* ',$OA= D9*+<(H'O 8?'N9 ?(+A*:/,

/$* , &'/+8-$%'O +*?*D;*A( ;:= &A(;@*++, - +=0 -=?(08+*?*D;*@+=0 >/D,- , ;=$HA=.

8 -=)( ;8;*:*@+8>8 ;*:*'=+( ?(+A*:/ 98C+/ :8D ) ,$='= +/ ;:%98A('+ ,, A:(>$, ,

;,)A8-88?:/D+,.

!-=@/7+8 ?(+A*:/ &A$/)/H'O&% D )-80 @/&'=+: -*:0+O8U - ;:=D9/'=@+8U /?8

G=$,+):=@+8U , +=C+O8U - D-(C(H @8H )8+=D( ()8 -=;(&A+=0 8'-8:,-) ( -=), ;,:/9,)=, A8+(&/

/?8 &.*:= (9/$H+8A 40). := +*-*$=@A,7 >$=?=+, ?(+A*: 98C* +* 9/'= -*:0+O8U

G=$,+):=@+8U /?8 ;:=D9/'=@+8U @/&'=+=.

/$H+8A 40

8:9/ ?(+A*:/ ;8-=++/ ?('= '/A8H, S8? 78>8 98C+/ ?($8 G,$A89 D/-/+'/C='= ,

:8D-/+'/C='=; ( +O89( +* ;8-=++8 ?('= «9*:'-=0» D8+, ( %A=0 -/+'/C (':/@/N :(0$=-,&'O ,

+* 98C* -=-/+'/C(-/'=&% D ?(+A*:/. (+A*:= ;8-=++, ?('= ;:8&', ;8 A8+&':(AG,U ,

)8->8-,@+,; U0 -=>8'8-$%H'O 9*'/$*-=9=, ,D D?,:+8>8 D/$,D8?*'8+( /?8 A89?,+8-/+=9=.

=;(&A 9/'*:,/$( 98C* ?('= 8)+8- , )-8&'8:8++,9, @*:*D -=;(&A+, 8'-8:= /?8 ':(?=,

:8D9,S*+, D?8A( ?(+A*:/ /?8 - 78>8 G*+':,.

*1 $

AS8 +/&=;+=7 -/+'/C (':/@/N :(0$=-,&'O ( ?(+A*:, @*:*D A(&A8-/',&'O, D$*C(-/++%,

D9*:D/++% , ' .,., 98C('O ('-8:='=&% &A$*;,++% -/+'/C( ?(+A*:/. A$*;,++% 98C('O

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

-=&'(;,- +/ -+(':,<+,7 ;8-*:0+,. $% :(7+/G,U &A$*;,+O , ;8$,;<*++% -=',A/++% -/+'/C,-

D/&'8&8-(H'O:

- *$*A':=@+,, 9*0/+,@+,, ;+*-9/'=@+, -,?:/'8:=, %A, -&'/+8-$HH'O&% +/ 9*'/$*-=0

&',+A/0 ?(+A*:/;

- ,+8), +=C+H @/&'=+( ?(+A*:/ D -,?:/'8:89 ;:(C+8 D'N)+(H ' O ,D -*:0+O8H

@/&'=+8H;

- :,D+89/+,'+, 9*0/+,@+, <(:8-8@+, (&':8U, %A, --8)%'O ( ?(+A*:;

- &',+A= ?(+A*:/ . ('*:(H'O >(98-=9 ;:8</:A89, 9,C &',+A8H , >(98-=9 ;8A:=''%9

N ;8-,':%+, ;8:8C+=+=.

A$*;,++% +/) 8'-8:89 98C('O ('-8:='=&% +* ',$OA= D >:()A8-=0 -/+'/C,-, /$* D

):,?+8.:/AG,7+=0, S8 -8$8),H'O &-%D+,&''H (9/$H+8A 41). &'/++, ;8%&+HH'O&% '=9, S8

+8:9/$O+/ +/;:(> / +/ ;$8S/)A/0, ;*:;*+)=A($%:+=0 $,+,U &A$*;,++%, ( D-'%DA8-=0 -/+'/C/0

98C* ?('= :,-+8 +($H ?*D ;8:(<*++% :,-+8-/>= &=;(@8>8 ',$/. /A=7 +/;:(C*+=7 &'/+

-=+=A/N, A8$= -=;(&A+=7 8'-,: ?(+A*:/ 9*+<* 9/A&=9/$O+8>8 8'-8:(, S8 8?:/D(N &A$*;,

>,):/-$,@+=7 :/), (& %A8>8:

=•

(1+sinr)/(g·_), (16.1)

* •

- ;8@/'A8-=7 8;,: -/+'/C( D&(-(;

r - :,> -+(':,<+O8>8 '*:'% -/+'/C(.

,+,9/$O+8 ;:=;(&'=9=7 >,):/-$,@+=7 :/),(& 8'-8:,- ?(+A*:,-, S8 9,&'%'O D-'%DA8-,

-/+'/C,:

=

´·R

, (16.2)

)* 

´=1,5...2 - A8*.,G,N+' +/),7+8&', -=',A/++%.

/$H+8A 41

$% )8?:* &=;(@=0 -/+'/C,- <=:=+/ 8'-8:( -=',A/++% -=D+/@/N'O&%:

=(3...6)/´, ;:=@89( 9*+<, D+/@*++% ;:=79/H'O )$% :%)8-=0 -/+'/C,-, / -*$=A, - )$%

&8:'(-/$O+=0; /´ - :8D9,: '=;8-8>8 <9/'A/.

AS8 -=;(&A+=7 8'-,: &A$*;88?:/D(H@8>8 9*+<, '8 )$% (&(+*++% ('-8:*++%

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

8$= -=&8'/ &A$*;,+O &'/N &(9,:+8U D >$=?=+8H ?(+A*:/, -=+=A/N %-=S* ':(?88?:/D8-/++%.

/) 8'-8:89 -=',A/++% ('-8:='O&% ;8:8C+=&'/ ':(? /, , ;8)/$O<* ;:%9(-/++% -/+'/C(

;:=;=+%N'O&%. * %-=S* 98C$=-8, A8$= -=&8'/ h ':(?= 9*+<* -=&8'= h

-,$O+8 &'8%@8U

-*:'=A/$O+8U &',+A=.

$% (&(+*++% &A$*;,++% D-'%DA8-=0 +/&=;+=0 -/+'/C,- >,):/-$,@+=7 :/),(& R&-

+/7?,$O<8>8 8'-8:(, S8 &'-8:HN &A$*;.

=',A/++% &=;( @=0 -/+'/C,- ,D N9+8&'*7

=',A/++% &=;(@=0 -/+'/C,- ,D ?(+A*:,- ?(-/N +8:9/$O+*, & (G,$O+* , >,):/-$,@+*. :=

+8:9/$O+89( -=',A/++, @/&'A= D+/08)%'O&% - ;:%9(- /++, $=<* - D8+, &'8-;/ 9/'*:,/$(,

:8D'/<8-/+8>8 +/) -=;(&A+=9 8'-8:89 ?(+A*:/.

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

-/+'/C( ;*:*9,S/H'O&% - G*+':/$O+( D8+(. /&=;+=7 -/+'/C, :8D'/<8-/+=7 ?,$% &',+8A

?(+A*:/, ('-8:='O D/&',7+, D8+=, ( A8':=0 78>8 @/&'A= +*:(089, )8'=, ;8A= $,7A/, S8

('-8:=$/&% +/ ;8-*:0+, -/+'/C(, +* )8&%>+* +=C+O8U @/&'=+= ?(+A*:/. ,> +/0=$( A8+(&/

$,7A= 8&=;( )8 >8:=D8+'/$, ;:=?$=D+8 )8:,-+HN :8>8-, ;:=:8)+8>8 (A8&( -/+'/C(; +/-A8$8

G*+':/$O+8>8 A/+/$( -/+'/C D+/08)='O&% - +*:(08989( &'/+,.

8:9/$O+* -=',A/++% -,)?(-/N'O&% - ?,$O<8&', &'/G,8+/:+=0 ?(+A*:,-, ( %A=0 :,>

+/0=$( &',+8A >8:=D8+'/$, ; 8?$=D( -=;(&A+8>8 8'-8:( &A$/)/N 45-558.

:= &(G,$O+89( -=',A/++, -&, @/&'A= -/+'/C( - ?(+A*:, D+/08)%'O&% - ;:%9(-/++,.

,$O+/ ;8-*:0+% &=;(@8>8 ',$/ - ?(+A*:, +* 9/N @,'A8 -=:/C*+8U $,7A=; (&, '8@A= G,NU

;8-*:0+, 8;(&A/H'O&% 8)+8@/&+8, ;:=@89( <-=)A,&'O 8;(&A/++% 8A:*9=0 @/&'8A +8&='O

&'/08&'=@+=7 0/:/A'*:. := &(G,$O+89( -=',A/++, - ?(+A*:, -,)&('+, D/&',7+, D8+=, S8

)8D-8$%N -=:,-+H-/'= ;8',A +/&=;+8>8 -/+'/C(, S8 +/)08)='O ( ?(+A*: +*:,-+89,:+8.

/A* -=',A/++% 9/N 9,&G* ;:= ;:8;(&A/++, +/&=;+=0 -/+'/C,- @*:*D ?(+A*:, &',+A=

%A8>8 +/0=$*+, )8 >8:=D8+'/$, ;,) :8>89 `=70...80‚.

 D/;8-+*+=0 ?(+A*:/0 ,D &(G,$O+=9 -=',A/++%9 ;:= -,)A:='', -=;(&A+8>8 8'-8:(

&;8@/'A( -=',A/++% N +8:9/$O+=9, ;8',9 D8+/ @/&'8A -/+'/C(, S8 :(0/H'O&%,

:8D<=:HN'O&%, &'-8:HH@= '/A D-/+=7 8?'N9 D/-/$*++%. 8$= 9*C/ 8?&%>( D/-/$*++% )8&%>+*

&',+8A ?(+A*:/, -=+=A/N &(G,$O+* -=',A/++%.

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

+/&=;+8>8 -/+'/C(. /&=@*++% +/&=;+8>8 -/+'/C( -8D)(089, S8 +/)/N 789( -=) & (&;*+D,U,

/ '/A8C ;:= ,+'*+&=-+,7 -,?:/G,U -/+'/C(, A8 $= 9/A&=9/$O+, ;:=&A8:*++% ;*:*-*:<(H'O

)*%A* A:='=@+* D+/@*++%, S8 -,);8-,)/N ;8:(<*++H &'/$8&', ?,@+8>8 '=&A( -/+'/C( +/

&',+A= ?(+A*:/. ,):/-$,@+* -=',A/++% 98C* 9/'= 9,&G* ;:= ?()O-%A89( +/0=$, &',+8A

?(+A*:/ )8 >8:=D8+'/$,, /C )8 +($O8-8>8 (>8:=D8+'/$O+* )+=S*).

+,$ .

=D+/@*++% '=&A( +/ &',+A= ?(+A*:,-.

=&A -/+'/C( +/ &',+A= D/$*C='O -,) -$/&'=-8&'*7 -/+'/C( , A8+.,>(:/G,U ?(+A*:/.

/7?,$O<* ;:8&'8 78>8 -=D+/@='= )$% -/+'/C,- ;8 -$/&'=-8&'%0, ?$=DOA=9 )8 :,)=+ (:,)A=7

?*'8+, ?(),-*$O+, :8D@=+= ).

A -,)898, >,):/-$,@+=7 '=&A :,)=+= (/?8 «,)*/$O+8 &=;(@8>8» 9/'*:,/$() +/ &',+A=

&()=+= +/ >$=?=+, h -,) :,-+% :,)=+= =_·g·h, )* _ - S,$O+,&'O :,)=+=.

$% :*/$O+8>8 &=;(@8>8 -/+'/C( -+/&$,)8A '*:'% @/&'8A 9,C &8?8H (-+(':,<+O8>8

'*:'%) , 8? &',+A= & ()=+= '=&A +/ &',+A= ('-8:HN'O&% 9*+<*:

=_·g·h·K,

)* K - A8*.,G,N+' :(0$=-8&', +/&=;+8>8 -/+'/C( , K=(1-sinr)(1+sinr)>1,

)* r - :,> -+(':,<+O8>8 '*:'%, ;:=?$=D+8 :,-+=7 :8>8-, ;:=:8)+8>8 (A8&( -/+'/C( -

&;8@=+A(.

=S*+/-*)*+, .8:9($= )/H'O +/?$=C*+* D+/@*++% '=&A( -/+'/C( +/ &',+A= ?(+A*:,-

;:= +*-*$=@A,7 U0+,7 >$=?=+,. 8 +*>$=?8A=0 (98-+8 -,)+8&%'O ?(+A*:/, >$=?=+/ %A=0 +*

;*:*-=S(N U0+O8>8 ;8;*:*@+8>8 :8D9,:(. $% ?,$O< >$=?8A=0 ?(+A*:,- G% D/A8+89,:+,&'O

;8:(<(N'O&% >8$8-+=9 @=+89 (+/&$,)8A D:8&'/++% &=$ '*:'% -/+'/C( 8? &',+A=, S8

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

-,)+8<*++% ;8;*:*@+8>8 ;*:*'=+( ?(+A*:/ F )8 78>8 ;*:=9*':/ L, '8?'8 @=9 9*+<*

>,):/-$,@+=7 :/), (& ;8;*:*@+8>8 ;*:*'=+( ?(+A*:/ R=F/L.

,&$% -=D+/@*+8U 9*C, >$=?=+= ?(+A*:/ 9/A&=9/$O+=7 >8:=D8+'/$O+=7 '=&A +/ &',+A=

+* D:8&'/N , ;:/A'=@+8 &'/?,$,D(N'O&%. =&A ;:%98 ;:8;8:G,7+8 S,$O+8&', -/+'/C( ,

>,):/-$,@+8>8 :/),(&/ 7 8?*:+*+8 ;:8;8:G,7+8 A8*.,G,N+'( '*:'% -/+'/C( 8? &',+A= ?(+A*:/

f: max=_·g·h/f.

/A&=9/$O+=7 -*:'=A/$O+=7 '=&A ?,$O<* >8:=D8+'/$O+8>8:

gmax=_·g·h/(K·f). (16.3)

 D-'%DA( D '=9, S8 D+/@*++%

D9,+HH'O&% ;:=?$=D+8 8?*:+*+8 ;:8;8:G ,7+8

,+<=7 ):(>( ( ,D D9*+<*++%9 :8>(



:8D9,: K D:8&'/N, / f (?(-/N), )$% ;:/A'=@+=0

:8D:/0 (+A,- ;:=79/H'O: K·f…const=0,2.

8), '=&A

max

=const…5_·R·g.

8D9,: -=;(&A+8>8 8'-8:( ($HA,-) ?(+A*:,- ;8-=++=7 ?('= )8&'/'+,9 )$%

D/?*D;*@*++% +*8?0,)+8U ;:8;(&A+8U &;:898C+8&',. 8)+8@/&, S8? (+=A+('= +*?*D;*A=

:,DA8>8 D/-/$*++% @*:*D 8'-,: -*$=A=0 9/& -/+'/C(, / '/A8C ;*:*8?'%C*++%9 D/'-8:,- ,

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

:= >:()A8-=0 +/&=;+=0 -/+'/C/0 ,D '=;8-8H A: (;+,&''H <9/'A,- «/» +/79*+<=7

:8D9,: -=;(&A+8>8 8'-8:( ;:%98A('+8U .8:9= ;8-=++=7 ?('=:

)$% )8++=0 8'-8:,- be(4,5…5,5)a;

)$% ?,@+=0 8'-8:,- ,D ;80=$=9 )8+G*9 be(4,5…6)a.

#-=)A,&'O +8:9/$O+8>8 -=',A/++% -/+'/C(:

a=5,65”]R

0,5

, (16.4)

)* ”=0,22...0,6 - 9*+<, D+/@*++% )$% ;=$*-=)+=0 , -8$8>=0 ;8:8<A8;8),?+=0, /

?,$O<* )$% >:()A8-=0 , D*:+=&'=0 -/+'/C,-.

:= >,):/-$,@+89( -=',A/++, <-=)A,&'O )8:,-+HN:

a=”](2gh)

0,5

)* h - -=&8'/ -/+'/C( - ?(+A*:,;

”=0,7...0,9 )$% :,)A=0 :8D@=+,- , ?*'8+(.

2,1 # " 

:8;(&A+/ &;:898C+,&'O ?(+A*:/ D/$*C='O -,) <-=)A8&', -=',A/++% &=;(@=0

-/+'/C,-. $% ?(+A*:,- ?*D(;=++8U ),U UU D+/0 8)%'O ;8 .8:9($,:

=3600a]_]•™, (16.5)

)* a - <-=)A ,&'O -=',A/++%, 8?(98-$*+/ (:/0(-/++%9 A(&A(-/'8&', -/+'/C(;

$% A:(>$8>8 8'-8: ( š=^(D-/™)

/4 ('(' D - ),/9*': 8'-8:();

)$% ;:%98A('+8>8 8'-8:( š=(

-/™)(

-/™) ('(' 

, 

- :8D9,:= &'8:,+ 8'-8:().

:8;(&A+/ &;:898C+,&'O ?(+A*:,-, S8 &;8:8C+%H'O&% ;:= A8C+89( -,)A:=',

D/'-8:/ (+/;:=A$/), )8D8-/+=0), 0/:/A'*:=D(N'O&% @/&89 U0+,7 ;:8;(&A+8U &;:898C+8&',

$% +89,+/$O+8>8 -=',A/++%:

/(_]a]š)=V

/(a]š), (16.6)

)* G

- :8D:/0(+A8-/ A,$OA,&'O -/+'/C( - ?(+A*:,, ';

- 8?&%> ?(+A*:/, 9

(+A*:+, D/'-8:=

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

/ - )*%A=0 -=;/)A/0 '/A8C )$% :*>($H-/++% -=0,)+8>8 @*:*D +=0 ;8'8A( +/&=;+8>8

-/+'/C(.

(+A*:+, D/'-8:= ;8-=++, D/)8-8$O+%'= '/A=9 -=98>/9:

- D:(@+,&'O 9/+*-:(-/++% , <-=)A,&'O ),U;

- S,$O+,&'O D/A:=-/++%;

- 98C$=-,&'O :*>($H-/++% ;8'8A( -/+'/C(;

- 9,+,9/$O+8 98C$=-, >/?/:='+, :8D9,:=;

- +*-*$=@A, D(&=$$% +/ -,)A:=''% , D/A:=-/++% D/'-8:/;

- +*98C$=-,&'O &/98&',7+8>8 -,)A:=''%;

- ;:=&'8&8-/+,&'O )8 D/&'8&(-/++% )=&'/+G,7+8>8 7 /-'89/'=@+8>8 A*:(-/++%.

$/&=.,A/G,% , A8+&':(AG,% D/'-8:,-

8 D/&8?, ),U D/'-8:= :8D),$%H'O +/ )-, >:(; =: -,)0:*SHH@, ;8',A ;8-,':% '/ &A$/)/H@,

;,);8: (9/ $H+8A 42).

/$H+8A 42

8 ;*:<8U, ?,$O< @=&$*++,7 >:(;, &'/-$%'O&% D/'-8:= ( -=), ;$8&A8U D/&(-A= ,

&*A'8:+,.

!/'-8:= ( -=), ;$8&A8U D/&(-A= (9/$. 42 /,?), -&'/+8-$H-/+, - )+=S* /?8 ?,@+=7

&',+G, ?(+A*:/, 0/:/A'*:=D(H'O&% +/7?,$O<8H A89;/A'+,&'H, /$* 9/H'O 0=?( - D+/@+=7

8;,: ( ;/D/0 ;:= -,)A:=-/++, , D/A:=-/++,, '89( U0 D/&'8&8-(H'O ',$OA= ;:= +*-*$=@A89(

8'-8:, , +*D+/@+89( '=&A( +/ D/'-8:. ,D+8-=)89 ;$8&A8>8 D/'-8:/ N &':,@A8-=7

>(&*+=@+=7 D/'-8: (9/$. 42 -), S8 &A$/)/N'O&% D ?*DA,+*@+8U A8+-*N:+8U &':,@A=,

+*:(0898 (A:,;$*+8U D 8)+,NU &'8:8+= - A:/7A= -=;(&A+8>8 8'-8:( ('8@A/ ), , :(0$=-8U

:/9= D )-89/ ?/:/?/+/9= 9/$8>8 ),/9*':/ 7 8;8:+=9= :8$,A/9=. := ;*:*&(-/++, :/9= -

'( /?8 ,+<( &'8:8+( 8'-,: D/A:=-/N'O&% /?8 -,)@=+%N'O&%, ;:=@89( &':,@A/ ;*:*A8@(N'O&%

;8 :8$,A/9, /$* A8-D/++% UU ;8 -/+'/C, -,)&('+,0.

/9/ D/'-8:/ ;*:*9,S/N'O&% >8:=D8+'/$O+8-:*7A8-8H ;*:*)/@*H. := ;:%9(-/++,

:/9= (;:/-8 -*:0+% >,$A/ &':,@A= )8 A,+G*-8>8 ?/:/?/+/ D/$=</N'O&% +*:(0898H, /

+=C+% :(0/N'O&% -;:/-8, S8 &(; :8-8)C(N'O&% &A8:8@*++%9 ),$%+A= -*:0+O8U >,$A=, S8

D+/08)='O&% +/) 8'-8:89, &':,@A=, , -=;(&A+=7 8'-,: ;8&'(;8-8 -,)@=+%N'O&%.

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

;8-*:'/H'O&% +/-A8$8 >8:=D8+'/$O+8U 8&, (9/$. 42 >, ), *), '/A S8 '*:'% U0 ;8 ;/D/0

-,)&('+,0, / 8'C*, 8;,: 9/+*-:(-/++H D+/@+8 9*+<*, @=9 8;,: ;$8&A8U D/&(-A=. /

-*:'=A/$O+89( -=;(&A+89( ;/':(?A( >8$8-+=9 @=+89 ( D/$*C+8&', -,) 78>8 )8-C=+=

-&'/+8-$HH'O 8)+8- /?8 )-(&*A'8:+, D/'-8:= D ;:%9(-/++%9 &*A'8:/ +/>8:( /?8 (+=D

(9/$. 42 C, D).

!/'-8: ,D ;:%9(-/++%9 ;:= -,)A:=-/++, +/>8:( +/) ; 80=$8H ;$8S=+8H, ;8 %A,7

&A8-D/N -/+'/C, )/N 98C$=-,&'O ;:= +*;8-+89( -,)A:='', :*>($H-/'= ;8',A -/+'/C( , /$*

9/N ', C 0=?/, S8 ;:= 78>8 D/A:=-/++,, 98C$=-8 D/S*9$*++% <9/'A,- -/+'/C( 9,C

A:89A8H &*A'8:/ , ;$8S=+8H A8-D/++%. !/'-8: ,D ;:%9(-/++%9 (+=D G,NU 0=?= +* 9/N, /$*

@*:*D +/%-+,&'O ;8:8>/ ;:= +*;8-+89( -,)A:='', D+/@+8 >,:<* :*>($H N ;8',A -/+'/C(.

$% -*$=A8A(& A8-=0 -/+'/C,- D/&'8&8-(H'O D)-8N+=7 &*A'8:+=7 D/'-8:, S8 9/N

;*:*-/>= D/D+/@*+=0 )-80 '=;,- (9/$. 42 =).

:= 78>8 -,)A:='', 8;(&A/N'O&% G,$A89 9*+<=7, +=C+,7 &*A'8:, , ;8',A -/+'/C(

:*>($HN'O&% ;8$8C*++%9 -*:0+O 8>8 -*$=A8>8 &*A'8:/; ;:= D/A:=-/++, &;8@/'A(

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

;,)+,9/N'O&% +=C+,7, S8 ;*:*<A8)C/N ;8)/$O<89 ( -=',A/++H -/+'/C(.

,D+8-=)89 &*A'8:+8>8 D/'-8:/ N ;/$OGO8-=7 D/'-8: (9/$. 42 A), S8 &A$/)/N'O&% D

8A:*9=0 -/CA=0, ;,)-,<*+=0 A8C+=7 +/ &-8N9( $/+GHD,, -=>+('=0 , D/>8&':*+=0 +/ A,+G,

-/C*$,- (;/$OG,-). /$OG, ;:= 8;(&A/++, $*>A8 ;:8+=A/H'O ( '8-S( -/+'/C(, / ;8;/-<=

+/ D+/@+=7 <9/'8A, D/'=&A/H'O 78>8 +/ ;$8S=+, $8'A/, D/A:=-/H@= -=;(&A+=7 8'-,:.

:= -,)A:='', D/'-8:/ ;/$OG, ;,)+,9/H'O&% $/+GH>/9= -,) 8)+8>8 ;:=-8)(: &;8@/'A( ',,

S8 8;( &A/$=&% +=C@*, / ;8',9 (&, :/D89.

0*9/ D/'-8:/ ):(>8U >:(;=, S8 ('-8:='O ;,);8: ;8-8:8'89 </:+,:+ 8>8 $8'A/.

!/'-8:= GO8>8 '=;( ;:= D/A:=-/++, +* D/S*9$%H'O <9/'A,- -/+'/C( , ;:=;(&A/H'O

:*>($H-/++% ;8'8A( -/+'/C( D9,+8H :8>( +/0=$( $8'A/. :8'*, -8+= 0/:/A'*:=D(H'O&%

-*$=A=9= >/?/:='+=9= :8D9,:/9=.

8 :8)( ;:=-8)( D/'-8:= :8D),$%H'O +/ :( @+, , 9*0/+,@+,. &'/++, ?(-/H'O

*$*A':=@+=9=, ;+*-9/'=@+=9= , >,):/-$,@+=9=. &, -=)= D/'-8:,- ,D 9*0/+,@+=9

;:=-8)89 98C('O ?('= D )=&'/+G,7+=9 ;:=-8)89.

=&A +/ D/'-8:= ?(+A*:,-, S8 9,&'%'O ;8$(C=)A, 9/'*:,/$=, -=D+/@/H'O %A '=&A +/

&',+A= ?(+A*:,-. =&A +/ D/'-8:= &=;(@=0 -/+'/C,- D/$*C='O -,) C8:&'A8&', A8+&':(AG,U

D/'-8:/ , ;:8G*&( D/;8-+*++% ?(+A*:/, '89( '8@+=7 78>8 :8D:/0(+8A N &A$/)+8H

D/)/@*H.

*:*)+,7 '=&A +/ >8:=D8+'/$O+=7 D/'-8: ()$% +/?$=C*+=0 :8D:/0(+A,-):

=5,6K

·g·_]R

´, (16.7)

)* K

- A8*.,G,N+' :,-+=7 2 )$% ?(+A*:,-, S8 &;8:8C+%H 'O&% -G,$89( ;:= A8C+89(

-,)A:='', D/'-8:/; 1 - )$% +*&;:8C+%N9=0 G,$A89 ?(+A*:,-; 1,5 - )$% ?(+A*:,-, S8

&;8:8C+%H'O&% +* ;:= A8C+89( -,)A:='', D/'-8:/;

´ - >,):/-$,@+=7 :/),(& -=;(&A+8>8 8'-8:(.

=&A +/ ;80=$, , -*:'=A/$O+, D/'-8:=:

=5,6K

·g·_]R

´(cos

`+m

´·sin

`), (16.8)

)* ` - :,> +/0=$( D/'-8:/ )8 8?:,H;

´ - A8*.,G,N+' :(0$=-8&', +/&=;+8>8 -/+'/C(; m

´=0,18/f ('(' f - A8*.,G,N+'

-+(':,<+O8>8 '*:'% +/&=;+8>8 -/+'/C().

=;(&A +/&=;+8>8 -/+'/C( @*:*D D/'-8: )8:,-+HN '-8:8-, ;$8S, -=;(&A+8>8 $HA/

+/ <-=)A ,&'O -=',A/++%. #-=)A,&'O -=',A/++% +/&=;+8>8 -/+'/C( - ;8:,-+%++, D,

<-=)A,&'H -=',A/++% :,)=+= D9*+<(N'O&% '=9 ?,$O<*, @=9 ?,$O<* A 8*.,G,N+'

-+(':,<+O8>8 '*:'% -/+'/C(. * -:/08-(N'O&% --*)*++%9 ( .8:9($( <-= ) A8&', -=',A/++%

:,)=+= A8*.,G,N+'/ ”

a= ”

](2P·g/_)

0,5

)* P - '=&A +/&=;+8>8 -/+'/C(, ƒ=_·g·h.

8 &;:/-8@+=9 )/+=9 ”

=0,65 )$% &(08>8 ;,&A(; ”

=0,55 )$% D*:+/; ”

=0,4 )$% -(>,$$%;

”

=0,3 )$% :()=.

Œ=-=$O+=A= , )8D/'8:=

Œ=-=$O+=A= ;:=D+/@*+, )$% ?*D(;=++8>8 , :,-+89,:+8>8, ,+8), :*>($O8-/+8>8,

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

(&'/'A(-/++% (?*'8+8D/9,&+=A,- ?*D(;=++8U ),U), S8 ;8' :*?(N :,-+89,:+8>8 /?8

:*>($O8-/+8>8 C=-=$O+=A/. :,9 '8>8, C=-=$O+=A=, D/&'8&8-(-/+, - :8D-/+'/C(-/$O+=0 ,

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

-/+'/C( +/ :8?8@( ;8$8'+=+( , :8D,>+/'= -/+'/C( )8 <-=)A8&',, :,-+8U <-=)A8&',

:8?8@8U ;8$8'+=+=.

,$O<,&'O '=;,- C=-=$O+=A,- +* ; 8':*?(H'O 8A:*98 ?(+A*:+=0 D/'-8:,-, '89( S8

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

@*:*D 8'-,:.

Œ=-=$O+=A= 0/:/A'*:=D(H'O&% -*$=A8H :8D9/U',&'H '=;,-, S8 -=?=:/H'O&% -

A8C+89( 8A:*989 ( -=;/)A( - D/$*C+8&', -,) :8)( , -$/&'=-8&'*7 -/+'/C(, S8

;8':*?(-/N'O&% ;:8)(A'=-+8&', , 9,&G*-=0 (98-.

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

;$/&'=+@/&'=0, &A:*?A8-=0, >-=+'8-=0 '/ ,+<=0. Œ=-=$O+=A= -,):,D+%H'O&% -,)

8)+879*++=0 A8+-*N:,- 9*+<8H )8-C=+8H, S8)8 ;,)-=S*+8H ;8'(C+,&'H )-=> (+/ ,

':=-A,&'H, '89( S8 -8+= 98C( 'O -,)@(-/'= '=&A -/+'/C( ;,) 8'-8:89 ?(+A*:/ /?8 $,7A=,

;*:*9,S/H'O -/+'/C ?,$O< '8-&'=9 ;:8</:A89 , ;*:*?8:HH'O -*$=A, 8;8:= ;:=

:8?8@89( ;:%9(-/++,. Œ=-=$O+= A= G,NU >:(; = ,+8), &$( C/'O 8)+8@/&+8 , A8+-*N:/9=,

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

+</ >:(;/ C=-=$O+=A,-

- ?/:/?/++,, )=&A8-,, $/+GH>8-, , $8;/'*-, +* 9/H'O

;:8'8'=;,- &*:*) A8+-*N:,- , 98C('O &$( C='= ',$OA= )$% -=)/@, -/+'/C( ?*D;8&*:*)+O8 -

8'-8:( ?(+A*:/.

':,@A8-, C=-=$O+=A= 98C('O ?('= >8:=D8+'/$O+=9= , ;80=$=9= D ;:%9(-/++%9

+/>8:( /?8 (+=D (9/$. 43 /). ,) &':,@A8-=0 A8+-*N:,- -8+= -,):,D+%H'O &% :8D'/<8-/+=9=

+/ ?$=DOA,7 -,)&'/+, ):(> -,) ):(>/ :8$,A88;8:/9=, ;:= +*-*$=@A,7 )8-C=+, -,)&('+,&'H

:8$,A88;8: +/ 8?*:+*+,7 >,$G,. /%-+,&'H, %A ;:/-=$8, +*:(089=0 ?8:',- ,, D/ -=+%'A89

;:=&A8:H-/$O+=0 C=-=$O+=A,-, 9/$8<-=)A8&', &':,@A= (0,05-0,45 9/&).

':,@A8-, C=-=$O+=A= D/&'8&8-(H'O >8$8-+8H (%-8H ;:= ;*:*9,S*++, D*:+=&'=0,

):,?+8- , &*:*)+O8A(&A8-=0 -/+'/C,-. *>($H-/++% ;:8)(A'=-+8&', )8&%>/N'O&% D/

)8;898>8H ;*:*&'/-+8U D/&(-A= /?8 D9,+8H <-=)A8&', &':,@A=. +8), C=-=$O+=A

;8&'/@/H'O -/>8-=9 (&':8N9, ;8 ;8A/D+=A( %A8>8 /-'89/'=@+8 :*>($HN'O&% <-=)A,&'O

&':,@A=, S8 D/?*D;*@(N D/)/+( -=':/'(. 8 ;*:*-/> &':,@A8-=0 C=-=$O+=A,- &'/-='O&%

+/),7+,&'O, +*-*$=@A/ 9/&/ , <=:8A=7 ),/;/D8+ ;:8)(A'=-+8&',. 8D:/0(+8A &':,@A8-=0

C=-=$O+=A,- /+/$8>,@+=7 :8D :/0(+A( &':,@A8-=0 A8+-*N:,-.

-=+'8-, C=-=$O+=A= (9/$. 43 ?) 9/H'O G,$O+8&',++=7 >-= +', D98+'8-/+=7 +/ )-80

;,)<=;+=A/0 , 8?*:'8-=0 ( D/A:='89( C8$8?, /?8 ':(?,. $% ;8$*> <*++% ;:%9(-/++%

-/+'/C( >-=+' -=A8+(H'O ,D 9/$=9 A:8A89, / ,+8), - )-(-0, )+=7 . -=+'8-, C=-=$O+=A=

-=A8:=&'8-(H'O )$% ':/+&;8:'(-/++% ;=$*-=)+=0, D*:+=&'=0, / '/A8C ):,?+8A(&A8-=0

+/&=;+=0 -/+'/C,-.

*:*-/>8H G=0 C=-=$O+=A,- N >*:9*'=@+,&'O, / 0=?8H - <-=)A* D+8<(-/++% >-=+'/

, $8'A/, / '/A8C -=&8A/ *+*:>8N9+,&'O. :8)(A'=-+,&'O :*>($HH'O D9,+8H @/&'8'=

8?*:'/++% >-=+'/ /?8 D/&(-A8H - >8:$8-=+ , ?(+A*:/.

/$H+8A 43

$/&'=+@/&', C=-=$O+=A= (9/$. 43 -) 0/:/A'*:=D(H'O&% -=&8A8H ':=-A,&'H ,

98C('O D/&'8&8-(-/'=&% ;:= ;*:*9,S*++, -/CA=0, -*$=A8A(&A8-=0 , /?:/D=-+=0

-/+'/C,-, +/;:=A$/), :%)8-8U , -*$=A8A(&A8-8U :()=. =?= ;$/&'=+@/&'=0 C=-=$O+=A,- -

-*$=A/ 9/&/ , -=&8A/ -/:',&'O.

/:/?/++, C=-=$O+=A= (9/$. 43 C) 9/H'O +/7?,$O<* ;:8&'( A8+&':(AG,H. 0

D/&'8&8-(H'O ,D >$/)A8H ;8-*:0+*H ?/:/?/+/ )$% )8?:* &=;(@=0 D*:+=&'=0 ,

):,?+8A(&A8-=0 -/+'/C,- , D :*?:=&'8H ;8-*:0+*H ?/:/?/+/ - )$% -*$=A8A(&A8-=0

-/+'/C,-. :8)(A'=-+,&'O C=-=$O+=A,- ;:8;8:G,7+/ ;*:*'=+( ;:8</:A( -/+'/C( ,

<-=)A8&', +/ 8A:(C+8&', ?/:/?/+/.

=?/ - -*$=A/ -=&8'/ ;/),++% -/+'/C( +/ :8?8@=7 8:>/+ A8+-*N:/.

 ?/>/'O80 -=;/)A/0 ;8':*?(-/H'O&% C=-=$O+=A=, S8 98C('O /-'89/'=@+8

;,)':=9(-/'= D/)/+=7 - /+'/C8;8',A. 8 D/&8?, ),U U0 :8D),$%H'O +/ )-/ '=;=:

1) ;:%98U ),U D -/>8-=9 *$*9*+'89, S8 -;$=-/N D/ )8;898>8H 9*0/+,@+8U

(A,+*9/'=@+8U) D-'%DA( +/ 8:>/+, S8 :*>($HN -/+'/C8;8',A;

2) +*;:%98U ),U, '*C ;8&'/@*+, -/>8-=9 *$*9*+'89, /$* -;$=- +/ 8:>/+, S8 :*>($HN

-/+'/C8;8',A, ;:8-/)='O&% &'8:8++,9 )C*:*$89 *+*:>,U.

Œ=-=$O+=A ;*:<8>8 '=;( D98+'8-/+=7 +/ 8)+,9 ;$*@, (A:,;$*+8U :/9= (A8:89=&$/),

+/ ,+<89( ;$*@, %A8U ;:=9,S*+=7 S8 ;*:*&( -/N'O&% ;:8'= -/>/ +/)/+ +/ 9/$H+A( 44, /. !

:/98H &;8$(@*+ ;,)8798-=7 9*0/+,D9 D/&(-A=, S8 -,):=-/N 8'-,: '=9 ?,$O<*, +,C +/

?,$O<89( ;$*@, -&'/+8-$*+/ ;:8'=-/>/. := GO89( D ?, $O <(N'O &% '8-S=+/ ;:8</:A(, S8

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

 C=-=$O+=A( ):(>8>8 '=;( :/9/ A8:8'A8>8 &':,@A8-8>8 -/>8-8>8 A8+-*N:/ D 8)+,NU

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

/+'/C +/ -/>8-=7 A8+-*N: ; 8)/N'O&% :*>($O8-/+=9 *$*A':89/>+,'+=9 -,?:/G,7+=9

C=-=$O+=A89. =>+/$ -,) )/'@=A/ ;*:*)/N'O&% +/ (&':,7, S8 :*>($HN &=$( '8A(, S8

;='/N *$*A':89/>+,' -,?:/G,7+8>8 C=-=$O+=A/, (+/&$,)8A @8>8 -,);8-,)+8 D9,+HN'O&%

78>8 ;:8)(A'=-+,&'O.

/$H+8A 44

1 – ;:8'=-/>/, 2 – ?(+A*:, 3 – D/&$,+A/, 4 – &':,@A/, 5 - </:+,:+/ 8;8:/; 6 – :/9/, 7 -

-,?:/G,7+=7 C=-=$O+=A, 8 - (;:(>8-9/>+,'+=7 )/'@=A, 9 – &':,@A8-=7 -/>8-8U A8+-*N:, 10

- :*>($HH@=7 (&':,7, 11 - (;:(>8-9/>+,'+=7 )/'@=A

8D/'8:/9= +/D=-/H'O&% (&':8U G=A$,@+8U ),U, S8 :8?$%'O ;:= A8C+89( G=A$,

-=)/@( D ?(+A*:/ -=D+/@*+8U A,$OA8&', ()8D=) +/&=;+8>8 -/+'/C(.

8D(-/++% 98C* ;:8-/)='O&% ;8 8?&%D, /?8 ;8 9/&,. 8D(-/ ++% ;8 8?&%D,

D),7&+HN'O&% D/ )8;898>8H 9,:+8U &()=+=, ;$ (+C*: / /?8 %@*,&'8>8 ?/:/?/+/. ,:+/

&()=+/ ;8-*:'/N'O&% ;+*-98G=$,+):89, ;:= GO89( 78>8 G=$,+):=@+/ &;=+A/ D/A:=-/N

8'-,: ?(+A*:/.

-'89/'=@+* )8D(-/++% ;8 9/&, ;:8-/)='O&% D/ )8;898>8H &()=+=, (&'/+8-$*+ 8>8

+/ -/>/0, S8 8?&$(>8-(H'O /-'89/'=@+, -;$=-= +/ ?(+A*:+=7 D/'-8: /?8 C=-=$O+=A (

989*+', A8$= 9/&/ +/&=;+8>8 -/+'/C( - &()=+, )8&%>/N D/)/+8>8 D+/@*++%. -'89/'=@+8

;:8-8)='O&% '/A8C -,)A:=''% , D/A:=-/++% -=;(&A+8>8 8'-8:( &()=+=, / ;8',9 '/A*

-,)A:=''% D/'-8:/ ?(+A*:/ /?8 -=9=A/++% C=-=$O+=A/.