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III. ȾɊȿȼȿɋɂɇɈȼȿȾȿɇɂȿ.
ɆȿɏȺɇɂɑȿɋɄȺə ɈȻɊȺȻɈɌɄȺ ȾɊȿȼȿɋɂɇɕ
674.023
Ⱥɥɟɤɫɚɧɞɪ Ⱥɧɚɬɨɥɶɟɜɢɱ Ɍɹɩɢɧ,
[email protected]
ɋɚɧɤɬ-ɉɟɬɟɪɛɭɪɝɫɤɢɣ ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣ ɥɟɫɨɬɟɯɧɢɱɟɫɤɢɣ ɭɧɢɜɟɪɫɢɬɟɬ
ɇȺɉɊəɀȿɇɂə ȼ ɉɂɅɖɇɈɆ ȾɂɋɄȿ
ɉɊɂ ɉɅȺɇȿɌȺɊɇɈɆ Ⱦȼɂɀȿɇɂɂ
Ɋɚɫɩɢɥɨɜɤɚ, ɤɪɭɝɥɵɟ ɩɢɥɵ, ɪɚɛɨɬɨɫɩɨɫɨɛɧɨɫɬɶ, ɭɫɬɨɣɱɢɜɨɫɬɶ, ɩɥɚɧɟɬɚɪɧɵɣ ɩɪɢɧɰɢɩ ɞɜɢɠɟɧɢɹ, ɧɚɩɪɹɠɟɧɧɨɟ ɫɨɫɬɨɹɧɢɟ.
Sawing, circular saws, efficiency, stability, circular saw differential motion,
tension.
.
[2].
,
,
,
,
,
-
,
[1].
Ɋɚɫɱɟɬ ɧɚɩɪɹɠɟɧɢɣ ɜ ɩɢɥɶɧɨɦ ɞɢɫɤɟ
ɨɬ ɞɟɣɫɬɜɢɹ ɰɟɧɬɪɨɛɟɠɧɵɯ ɫɢɥ ɢɧɟɪɰɢɢ
(
. 1).
:
, /
r 
2
v 2 3   
2 
2
2
1    x  2  ,
g 0,8 
x 
(1)
107
, /
r 
–
2
v 2 3   
1  3  2 
2

1   
,
g 0,8 
3   x2 
(2)
(7,85 / 3); v –
), / ;  –
(
( = 0,3);  –
,
,
, -
 = r / R; x = Ri / R, x –
(
, x = 0,2; 0,4; 0,6; 0,8; 1,0).
Ɋɢɫ. 1.
,
,
(
(
. 2, ɛ).
ɇɚɩɪɹɠɟɧɢɹ ɜ ɞɢɫɤɟ ɩɪɢ ɪɚɛɨɬɟ ɩɨ ɨɛɵɱɧɨɣ ɫɯɟɦɟ.
.1
:
D = 400
, R = 200
.
108
-
. 2, ɚ)
V
= 60 / ,
1
Ɋɚɞɢɚɥɶɧɵɟ ɢ ɬɚɧɝɟɧɰɢɚɥɶɧɵɟ ɧɚɩɪɹɠɟɧɢɹ ɜ ɩɢɥɶɧɨɦ ɞɢɫɤɟ
, R = 200
)
(V = 60 / , D = 400
x
r

1
25
200
0,125
0
26
2
25
200
0,5
9
12
3
25
200
1
0
6

r
(
. 3).
ɚ)
1
1
ɛ)
1
1
2
2
Ɋɢɫ. 2.
109
Ɋɢɫ. 3.
(
.
. 3),
-
:
1.
(
)
–
(
)
-
.
2.
.
3.
.
,
ό
(
)
.
ɇɚɩɪɹɠɟɧɢɹ ɜ ɞɢɫɤɟ ɩɪɢ ɩɥɚɧɟɬɚɪɧɨɦ ɞɜɢɠɟɧɢɢ.
4.
-
,
.
-
,
1
–1
,
2 –
Ω  1  2 ,
(3)
,
(
ω2 OC
=
,
ω1 O1C
Ɉ1ɋ –
110
, ; Ɉɋ –
–1
.
. 4)
(4)
, .
Ɋɢɫ. 4.
: O1a1 = 25
; O1a2 = 50
; O1a3 = 100
; O1a4 = 150
O1a5 = 200
; O1O = 1,72
; D = 400
; d = 50
,

n–
,
1
/
n
,
30
(5)
.
2
ɩ = 1400
:
D = 400
;
;
n = 2400
ɟ = 1,72
.
/
/
;
;
(5),
1 
2 
3,14 2400
 251 c1;
30
3,14 1400
 147 c1.
30
-
Ω  251  147  398
1
,
111
(
.
. 4)
ɟ = 1,72,
)
(
-
147

Ɉɋ
 2 
 0,586
Ɉ1ɋ
1 251
O2C  1,09
O1C = 0,63
.
Ω,
–1
,
-
,
V  ΩR,
V–
, –1; R –
,
(6)
/ ; Ω –
-
, .
,
.
. 4.
(1), (2).
,
.
ɚ1:

а
ɚ1ɋ –
O1C  0,63
Va1  Ωa1C ,
(7)
ɚ1,
d 50
ɚ1O1  
 25
2
2
ɚ1C  ɚ1O1  O1C ,
, a1C  25,63
,
.
Va  398  0,02563  10,2,

a1
R
:
X a1 
O1O –
,
112
, / :
O1O  O1a1
,
R
,
25
;R–
e  1,72
,
(8)
; O1a1 –
200
.
X a1 

,
1,72  25
 0,133,
200
25
 0,125.
:
200
(1)
« »
-
(2),
ɚ 1:
2
, /
:
7,85  104,64 3  0,3

9,81
0,8
r 
0,0156 

 1  0,1252  0,1332 
 0,42;
0,0176 

, /
 
2
:
7,85  104,64 3  0,3 
1  3  0,3
 0,0176 
1  0,00156 
9,81
8 
3  0,3
+
0,0156 
 0,44.
0,0176 
.
. 2.
2
Ɋɚɫɱɟɬ ɪɚɞɢɚɥɶɧɵɯ ɢ ɬɚɧɝɟɧɰɢɚɥɶɧɵɯ ɧɚɩɪɹɠɟɧɢɣ ɜ ɩɢɥɶɧɨɦ ɞɢɫɤɟ
ɩɪɢ ɩɥɚɧɟɬɚɪɧɨɦ ɞɜɢɠɟɧɢɢ
r,
H/
2
 ,
H/
2
V, /
V2
X
X2
ɚ1
10,20
104,06
0,133
0,0178
0,42
0,44
ɚ2
20,15
406,05
0,258
0,0669
9,58
9,96
ɚ3
40,05
1604,06
0,508
0,258
36,88
42,68
ɚ4
59,95
3594,09
0,758
0,575
48,99
77,94
ɚ5
79,85
6376,14
1,01
1,017
–3,58
87,19
113
:
1.
(
. 5)
,
,
.
,
(
,
. 3)
.
(
. 5)
.
, /
2
r
R,
Ɋɢɫ. 5.
2.
,
–
.
:
[3].
;
,
;
.
114
-
Ɉɩɪɟɞɟɥɟɧɢɟ ɧɚɩɪɹɠɟɧɢɣ ɜ ɞɢɫɤɚɯ ɩɢɥ ɨɬ ɧɟɪɚɜɧɨɦɟɪɧɨɝɨ ɧɚɝɪɟɜɚ
,
(
-
. 6).
:
, /
r
2
= (Δt  α  E) / (4  (1 – μ))  ((r2 – a2)  (b2 – r2) / (r2b2)),
, /
(9)
2
= (Δt  α  E) / (4  (1 – μ))  ((r2 + a2)  (b2 + a2) – (a4 – 3r4)/(r2b2)), (10)
t –
(Δt = 28  );  –
(11,6  10–6); E –
,
;a–
,
;–
(2  105
/ 2); r –
,
;b–
(0,3).
-
t, C
t = f(R)
R,
Ɋɢɫ. 6.
tmax = 28 C.
. 3.
115
3
Ɋɚɞɢɚɥɶɧɵɟ ɢ ɬɚɧɝɟɧɰɢɚɥɶɧɵɟ ɧɚɩɪɹɠɟɧɢɹ ɜ ɩɢɥɶɧɨɦ ɞɢɫɤɟ
ɨɬ ɧɟɪɚɜɧɨɦɟɪɧɨɝɨ ɧɚɝɪɟɜɚ
tmax E
4(1  )
a,
23,2
b,
25
200
r,
/
r,
26,72
51,72
101,72
151,72
201,72
2
,
2,84
16,59
16,16
9,58
–0,39
. 7 [1].
:
1)
;
2)
.
,
,
,
,
.
+ , /
2
r
R,
–
Ɋɢɫ. 7.
116
, /
2
2
42,62
24,32
6,96
–15,86
–46,88
,
,
/
-
-
,
.
.
,
.
-
. 8 [2].
Ɋɢɫ. 8.
,
(
. 8)
,
.
-
,
:
1.
,
,
,
,
-
,
.
.
[3].
2.
.
-
.
,
.
2,76 /
2
.
117
ȼɵɜɨɞɵ
:
1.
,
.
,
,
,
-
,
,
2.
,
.
,
-
,
,
.
3.
,
,
-
«
»
,
,
.
4.
.
Ȼɢɛɥɢɨɝɪɚɮɢɹ
1. ɋɬɚɯɢɟɜ, ɘ.Ɇ.
. .
. .:
.
2. Ɍɹɩɢɧ, Ⱥ.Ⱥ.
[
-
] /
, 1989. 384 .
-
[
]/ . .
//
. 2012.
. 201. . 153–165.
-
3. Ɍɹɩɢɧ, Ⱥ.Ⱥ.
[
] /
. 2012.
. .
//
. 203. . 91–99.
-
.
.
118
,
-
,
,
,
,
-
,
.
,
,
.
,
,
,
,
-
,
.
.
.
.
.
,
.
-
2
2,76 /
.
,
.
-
,
,
-
,
,
,
.
,
,
.
-
,
,
,
,
,
-
.
,
,
« -
»
,
,
.
,
.
***
Length cutting of wood by circular saws is very important for woodworking industry. Therefore, the study and improvement of this process is necessary for increasing circular machine efficiency. During the operation a saw has a complex stress state
119
due to the forces of cutting resistance, non-uniform heating on the disk radius, centrifugal tensions, bending oscillations and inherent stresses. Let’s look at the stresses in
the saw working in the standard way and working with differential motion. Radial
stresses are similar to usual way working stresses, but they have a larger maximum in
the middle of the disc. You can also note that the slope of curve is more uniform.
Stresses on the inner and outer radius are not equal to zero. Tangential stresses change
to the opposite in the middle of the disk, during normal rotation. At differential motion
of the saw stresses have a larger value. Total tangential stresses are distributed according to the sinusoidal curve. They are located in the same zone and don’t change
throughout the disc. Stress values at the inner and outer radius of the disk differ by
2.76 N/mm2. Stresses coming from the differential motion of the saw have a number of
positive qualities. Total tangential stresses are distributed on a disk with a slight difference in value don’t change and remain almost in a constant range. This fact suggests
that the tangential stresses stretch the saw in the longitudinal direction almost equally
from the tool bore to the tooth rim. This creates conditions for increasing the saw
stiffness and stability in the cut, especially for thin saws. The absence of stress eliminates thermal deformation. It has a positive effect on the thin saws, which are very
sensitive to uneven distribution of thermal stresses on the disk radius. Stress values
in a disk at differential motion is higher than normal, so the saw is more "loaded"
due to the presence of oscillatory factors in the longitudinal direction. Therefore,
there are prerequisites for increasing the stiffness of saw at work. Increasing the
stiffness and stability of the saw with a differential motion creates conditions for better application of thin saws.
120
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