Лекции по ТММ

§2.4 (

.

ϕ1 – " .

) 1-

.

%: ϕ1, ω1, lAB, lBC, lBS2, G2, G3, F3, IS1, IS2.

., ω1.

(

, , ,

.

! – .1; :

2.4.1.

(

$

:

= .

' $

$ .

= +

I × w2	= mi × vi2	+ Ii × wi2
2	2	2
3 !	3 ! .	3 ! 0.
	$0.	$0.

& :

I × w2 = m3 × vC2				+
2	2
I = m3	×	vC	2 + m2
	wM

m2 × vS22

+ IS2 × w22

+ IS1 × w12

2

2

2

2

w2

2

w1

2

×

vS2

+

IS2

×

+

IS1

×

wM

wM

wM

ω = ω1

I = m3 × vqC2 + m2 × vqS22 + IS2 × u221 + IS1

4.

I = I + I + I + I

1 2 2 3

( $

.

#		- " I ,
I2BP , :
	T2	= T!
	IS2 × w22	= I2 × w2
	2			2
		w2		2
				2
I2				= IS2 × u2 1
	= IS2 ×
	wM

2.4.2 .

–

".

– =

I2	× w2	ϕ
			(1)
	2	- = 2 d j
		j
(

(") ,

, "

,

, ".

M

d j1 = Fi d si + Mi d ji

| ×

1

d t

€

Mi × wi

M

× wM = Fi × vi × cos(Fi × vi ) +

vi

€

ωi

M

= Fi ×

× cos(Fi × vi ) + Mi

×

wM

wM

#

= Fi

€

+ Mi

−

M

× vqi × cos(Fi × vi )

× ui 1

& F3 – MF3 .

# - "

, MF3 ,

:

AM = AF3

M	€
	× ωM = Fi × vC × cos(Fi × vC )
M	€
	= Fi × vqC × cos(Fi × vC )

§2.5 &

$ ( " ).

(1) , ω

M	=		2 × (A		+ T )
				I

2.5.1 ( % ).

% M = f (j1 ) .

M .

0 M

:

,

, . ! " (#1)

"

.

m = mA × mA A OK

%% & % ( ε

).

- (1), (1)

" # ,

2 × ωM × I × dω

w2 × d I

dt

+

2 × dj

= M

| × dt

2 × dj

dw

2

wM × I

×

dt

w × d I

dj

+

2 × dj

= M

dt

M

d I

2

eM =

-

w

×

(3)

dj

2×I

2×I

d I

2.5.3 % .

d jM

I = f (j1 ) .

I	= I1	+ I2	+ I2 + I3
	I =	II	+	III
		const		var

&

i

$ . % $

i.

tg x =

c

d(yI / mI)

100

d yI

d I

mI

mI

=

= m

×

= m

× tg x

dj

d(

x

ϕ

/ m )

d xϕ

ϕ

ϕ

ϕ

d I

mI

c

= m

×

dj

100

ϕ

2.5.4ε %ω =f( 1).

ε= dω × dϕ = dω × w = wM × d(yω μω ) =

M dt dj dj d(xϕ mϕ )

= w

M

× mω

× d(yω )

= w

M

× mω × tg x

m

ϕ

d(x

ϕ

)

m

ϕ

$ tg x =

z

100

§2.6 2 .

)					) ( )

)

)

. 2.6

), ), ) ± ;) ± .

.

1 (2). 1 (3). & :

	ϕ % djM
	t =
		w	M
	ϕ

.

	w	=	ω max + ω min
			2

.

3## δ

d = ω max − ω min w

'$ δ $

:

	d =	1 ¸				1
						10
		5
	d =		1		¸				1
		20					50
	d =		1	¸					1
		50					100
	d =		1			¸				1
		100							500

( , )

( )

$

$

) 145 5.

%

	M =		2 × (A	+ T )		,
			I
	I	= II		+ III
			const	var

% ω

, $

δ, (II )& '

2.6.3 '% (II )& ' .

3 w w _max

w _min

$ (( I), :

(D TI)MAX =

(II )& ' × ω2 max

-

(II )& ' × ω2 min

=

(II )& '

2

2

=

× (

-

ω min

)× (

+

ω min

)

2

ω max

ω max

ω= ω max + ω min

2

δ = ω max − ω min

ω

(D

)

MAX

= ( )

× d ×

2

TI

II

& '

ω

(DTI)MAX

(II )& ' =

(2)

d × ω2

ω

=

p × n

; [ / ]

30

( w

(1) , . . , $

, ( . ).

§2.7 .

.

% :

1.;

2.( .%! 2).

:

3 - .

%:

F3, G1, S1, M 1, G2,

S2, 2, G3, S3,

wi, ei, vi, ai.

.:

1 Qij

! ,

. ' ,

( Q )

( Q - ).

2 ± ,

± q.

! 1

4 -

4 -

! 2

4 -

4 -

! 3

( %

Si = - mi × Sii = - εi × ISi

3 :

QCX = F3 + S3

QCY + Q34 = G3

2 :

X

X

X

QB

- QC

= S2

QY - QCY = S2Y + G2

´

2 -

C ´ q2 =

2

Q

Q

Q × Y - QY × X

- Q × qY + QY × qX =

2

2

2

C 2 C 2

1 :

		X				X			X
QA				- QB			= S1
QAY - QBY = S1Y + G1
			A ´			1 -			B ´ q1 -			1 =		1
	Q							Q
QA × 1Y - QAY × 1X - QB × q1Y + QBY × q1X - 1 = 1
:
								QAx		QAy		QBx				QBy	QCx	QCy	Q34	M1
F3+ S3							0			0		0				0	1	0	0	0		x
																						QAy
G3							0			0		0				0	0	1	1	0		QA
x							0			0		1				0	-1	0	0	0		x
y																						QBy
S2
S2 +G2				=			0			0		0y				1 x	0 y	-1 x	0	0		QBx
M 2							0			0		p2				-p2	-q2	q2	0	0		QC
S1x							1			0		-1				0	0	0	0	0		QCy
S2y+G2							0			1		0				-1	0	0	0	0		Q34
M 1								p1y		-p1x		-q1y				q1x	0	0	0	-1		M1
b																A						x

* 0.

§2.8 1

.

" - ,

" . * ,

" "

.

" ( ) .

2 , , ,

.

# "

:

∙., , - .

∙, - ! .

∙, , - $ .

2.8.1 ( & .

5

" . (

" Q21 "

! ϕ

.

	F =Qn12.tg ϕ
	tg ϕ= f
	F =Qn12.f

3## f $

.

2.8.2( " & .

1 -

r* -

( -

ρ - ;

ρ = 1

3 1 O1C = sin ϕ 1 = 1 sin ϕ

O1K

Mc= Q12. 1 = Q12. r*.sin ϕ

( ϕ sin ϕ tg ϕ = f . :

Mc= Q12. r*.f

( " '( "

" ϕ

! ρ

) 145 6.

2.8.3 ) ! (η)

.

A* %+ .).

η = . . . .

A* %+ ).+

'(%

" .

η =	.				× ω - .,
	t	=	.	=		=
							!. × u .− -
	.		. !. × ω .,

t

u .− - = ωω ., h < 1- .,