кинематические соотношения в планетарном механизме

674.023
Ⱥɥɟɤɫɚɧɞɪ Ⱥɧɚɬɨɥɶɟɜɢɱ Ɍɹɩɢɧ,
[email protected]
-
ɄɂɇȿɆȺɌɂɑȿɋɄɂȿ ɋɈɈɌɇɈɒȿɇɂə ȼ ɉɅȺɇȿɌȺɊɇɈɆ
ɆȿɏȺɇɂɁɆȿ ɊȿɁȺɇɂə ɄɊɍȽɅɈɉɂɅɖɇɈȽɈ ɋɌȺɇɄȺ
Ɋɚɫɩɢɥɨɜɤɚ, ɤɪɭɝɥɵɟ ɩɢɥɵ, ɪɚɛɨɬɨɫɩɨɫɨɛɧɨɫɬɶ, ɭɫɬɨɣɱɢɜɨɫɬɶ, ɛɨɥɶɲɚɹ
ɜɵɫɨɬɚ ɩɪɨɩɢɥɚ, ɩɥɚɧɟɬɚɪɧɵɣ ɩɪɢɧɰɢɩ ɞɜɢɠɟɧɢɹ.
Sawing, circular saws, efficiency, stability, high length of stroke, circular saw
differential motion.
ȼɜɟɞɟɧɢɟ.
-
.
.
.
.
.
–
–
,
,
.
.
. 1.
Ɍɪɚɟɤɬɨɪɢɹ ɪɟɡɚɧɢɹ ɜ ɤɪɭɝɥɨɩɢɥɶɧɨɦ ɫɬɚɧɤɟ ɫ ɤɪɭɝɨɜɵɦ ɜɪɚɳɟɧɢɟɦ ɩɢɥɵ.
–
.
.
,
( )
(
)
( . 2).
153
. 1.
. 2.
–
-
O–
R,
.

*
.
154
.:
A
R
*
t
 x1  R sin  A  R sin t ,

 y  R cos  A  R cos t.
. .
, 2002. 584 .
(1)
.
(
x–
)
.
vs
-
 x2  vst ,

 y2  0.
(2)
(
)
:
-
.
(1), (2)
 x  x1  x2  R sin t  vst ,

 y  y1  y2  R cos t.
:
(3)
1(
. 3).
1', 2', 3'
-
. .
(
tz = D / z,
D–
,
):
(4)
; z–
,
.
,
,
( . .
),
( ):
Tz = 60 / nz,
n –
, .
(5)
,
/
; z –
,
,
(
):
Uz = 103vs / nz,
3
10 –
vs –
z–
(6)
(
, /
.
,n–
,
/
),
;
155
. 3.
2(
2–2,
4–4,
Sz ,
3Sz
.
. 3)
3–
3–3,
. .
2Sz ,
2, 3, 4
1
4–
. .,
1.
.
,
,
Sz ,
(
),
-
.
(
Sz ,
)
.

e
e  S z sin .
(7)

.
,
.
-
,
,
-
.
–
.
Ɍɪɚɟɤɬɨɪɢɹ ɪɟɡɚɧɢɹ ɜ ɤɪɭɝɥɨɩɢɥɶɧɨɦ ɫɬɚɧɤɟ ɫ ɩɥɚɧɟɬɚɪɧɵɦ ɞɜɢɠɟɧɢɟɦ ɩɢɥɵ.
156
.
–
,
–
,
.
P
:
 X  r sin 1t  R cos(t (1  2 ))  vst ,

Y  r cos 1t  R sin(t (1  2 )),
r–
(8)
(
 –
); R –
(
(
)
);
OX;  –
-
.
X
( / ):
Y –
Vx  r1 cos 1t  R(1  2 )sin(t (1  2 ))  vs ,

Vy r1 sin 1t  R(1  2 ) cos(t (1  2 )).
X
(9)
Y( / )
Ve  Vx2  Vy2 .
(10)
. 4.
157
1 (
1', 2', 3'
. 5).
. .
,
,
,
(5).
,
,
Uz
OY
(
 x  U z  r sin1t ,

 y  r cos 1t.
):
2(
Sz ,
2–2,
OX
(11)
. 5)
OX
OY,
3–
2Sz ,
1
1.
.
. 5.
2, 3, 4
3–3,
. .
. .,
-
, 1/2 = 2
Ʉɢɧɟɦɚɬɢɱɟɫɤɢɟ ɫɨɨɬɧɨɲɟɧɢɹ ɜ ɩɥɚɧɟɬɚɪɧɨɦ ɦɟɯɚɧɢɡɦɟ ɪɟɡɚɧɢɹ.
,
,
,
,
158
,
-
,
.
.
-
.
–1
(
1
)
 = 1 + 2 .
2 –
(12)
,
VA  ΩCA.
VA –
,
–1
.
( / )
(13)
/ ;
–
, .
,
,
,
-
,
.
-
– K:
K
n
2 –

n
n
(14)
; 1 –
–
,
1
,
2
.
U (
U ( /
;
–1
)
)
(
),
.
(
)
U  U  e,
U –
(15)
-
,
; –
,
.
159
. 6.
R–
,e–
,
= ,
1
1
= R;
() C–
,
,
K,
-
.
K
,
,
.
,
1 O1C
,

2 OC
1
(
-
. 6):
(16)
–
1 = 2 , . .
, ;
–
, .
,
1
/
= 1.
(
. 7).
,
.
K = 1,5
K = 2,5
. 8.
. 9.
160
, 1 = 2
. 7.
K = 2,5
. 8.
.
. 6.
K = 2,5.
( –1).
V = 60 / , D = 500
,e=5
 = V / CA,
V–
(17)
, / ; CA –
A
,
C, .
161
. 9.
CA
CA 
CA 
( ):
eK  R ( K  1)
,
( K  1)1000
(18)
52,5  250(2,5  1)
 0, 253.
(2,5  1)1000
Ω
60
–1
 240 c .
0, 25
(12),
(
–1
):
2 
2 
Ω
,
K 1
(19)
240
–1
 68 c .
2,5  1
1 = K2 ,
(
–1
1 2,5 68  170 c–1.
162
)
(20)
n

n
n
(
  30
;

–1
)
(21)
68  30
 650,
3,14
170  30

 1624 .
3,14
50–60–70
.
5–15–45
/
Ɋɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɨɜ ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɫɤɨɪɨɫɬɟɣ ɪɟɡɚɧɢɹ
ɢ ɜɟɥɢɱɢɧ ɷɤɫɰɟɧɬɪɢɫɢɬɟɬɨɜ
V, /
I
II
e,

1
,
–1
2
K
–1
,
n
n
50
5
198
99
99
1,0
946
946
50
15
193 116
77
1,5
738
1107
50
45
177 127
51
2,5
484
1209
60
5
238 119 119
1,0
1135
1135
60
15
232 139
93
1,5
885
1328
60
45
213 152
61
2,5
581
1451
70
5
277 139 139
1,0
1324
1324
III 70
15
270 162 108
1,5
1033
1549
70
45
248 177
2,5
677
1693
71
D,
500
ȼɵɜɨɞɵ.
:
1)
,
;
2)
K  e  sin  t (
),
t –
3)
(
. 8)
,
K
e,
;
,
11  31
;
163
4)
.
-
,
;
1
K > 1;
5)
2
6)
;
7)
,
3000
8)
/
11 31 (
;
. 9)
-
.
,
,
.
.
-
.
.
.
:
;
;
.
:
,
,
(
,
,
,
,
.).
.
-
.
.
164
–
,
-
–
,
K = e  sin t (
,
),
.
t –
.
(
,
,
),
-
.
1
2
K > 1.
.
-
,
,
-
.
***
Length cutting of wood in circular saws is very important for woodworking industry. Therefore, the study and improvement of this process is necessary for increasing circular machine efficiency. Circular saws have many advantages as compared to frame
and belt saws. But during the operation they demonstrate some disadvantages. They are:
loss of stability, labour intensiveness when getting ready for work, malfunction of the
normal process of chip formation and chip removal from kerf at high length of stroke.
There are several ways of increasing stability of circular saws in wood sawing. They are
increasing the disc thickness, fogging, rolling and changing the saw design (making in
saw blades radial and tangential slits of various shapes; square and elliptical saws). To
ensure the circular saws stability, improvement formation and removal of chip we have
developed a new method. It’s based on the principle of circular saw differential motion.
Circular saw makes a plane-parallel motion with vibrations in the plane of rotation when running planetary gear. Circular saw moves in a complex way. The resulting
movement of the saw is composed of two rotational motions around parallel axes. One
of them is the axis of saw shaft; the other is an eccentric tail axis, which set the saw
blade. The cut pattern is a cycloid. Each loop of it is displaced vertically by an amount
= ∙ sin , mm, where ωt – angel angle of shaft rotation. When the eccentricity
increases, the curvature of the cycloid increases as well, which leads to a change in the
incidence angle. And the cutting speed increases as well as feed per revolution of the
saw. To improve the quality of chip formation and cutting surface a saw has to perform a few turns on the cutting arc per revolution of a saw shaft. There is an overlapping of cut patterns for the neighboring teeth on cutting arc when saw makes a differential motion. The cutting arc is divided into several sections, which helps to improve
the process of chip formation and chip removal from the kerf.
165