Conference Paper · March 023 citations reads 163 authors

The XXXVI International Scientific Symposium "Multidisciplinary Studies of the Turkish World" 
The 25
th
 of March 2023 ISBN: 978-605-72481-0-7 Eskishehir / Türkiye 
 
---186--- 
If we take the path of deceleration
𝑆
𝑡
=
𝑉
120
for light duty, we find the average deceleration time as 
follows: On the other side, 
𝑄 = 𝑐 ∙ 𝑚
3 
∆𝑡 (10)
here
𝑐 = 0,46 ∙ 10
3
𝐶𝑜𝑢𝑙 𝑘𝑞 ∙ 𝐾
⁄
- heat capacity is taken for steel. 
Let us assume that all the heat generated during braking is transferred only to the disks that are in motion.
Then 
𝒎
𝟑 
=
𝝅𝜹𝝈
𝟒
(𝑫
𝒙
𝟐
− 𝑫
𝟎
𝟐
)
(𝒛 − 𝟏)
𝟐
 
get. 
Taking into account expressions (9) and (10) in expression (8), we obtain: 
𝒄𝒎
𝟑
(𝒕
𝟐
− 𝒕
𝟏
) = 𝒌
𝑻
𝑻
𝟐
∙ 𝝎𝝉𝒗
 
or 
∆𝒕 = (𝒕
𝟐
− 𝒕
𝟏
) = 𝒌
𝑻
𝑻
𝟐𝒄𝒎
𝟑
∙ 𝝎𝝉𝒗 =
𝟒𝒌𝑻
𝑻
∙ 𝝎𝝉𝒗
𝒄𝝅𝝆𝒙
𝟐
(𝒙
𝟏
𝟐
− 𝒙
𝟒
𝟐
) ∙ (𝒙
𝟏
− 𝟏)
(𝟏𝟏)
 
get. 
If we write expressions (7) and (11) instead of them in expression (6), we get: 
𝒈
𝟎𝟑
= 𝒂
𝟑
∙ 𝜶𝑬(𝟏 − 𝝁
𝟐
) ∙
𝟒𝒌𝑻
𝑻
∙ 𝝎𝝉𝒗
𝒄𝝅𝝆
∙
𝟏
𝒙
𝟐
(𝒙
𝟏
𝟐
− 𝒙
𝟒
𝟐
) ∙ (𝒙
𝟏
− 𝟏)
 
or 
𝒈
𝟎𝟑
= 𝑪
𝟎𝟑
∙
𝟏
𝒙
𝟐
(𝒙
𝟏
𝟐
− 𝒙
𝟒
𝟐
) ∙ (𝒙
𝟑
− 𝟏)
(𝟏𝟐)
 
here 
𝑪
𝟎𝟑
= 𝒂
𝟑
𝒂𝑬(𝟏 − 𝝁
𝟐
) ∙
𝟒𝒌𝑻
𝑻
∙ 𝝎𝝉𝒗
𝒄𝝅𝝆
 
If we write expressions (3), (5) and (12) instead of expression (1), we will get the following 
expression for the objective function [6]: 
𝑔
0
= 𝑐
01
∙ 𝑥
2
∙ 𝑥
3
(𝑥
1
2
− 𝑥
4
2
) + 𝐶
02
(𝑥
1
2
− 𝑥
4
2
) ∙ (𝑥
3
− 1) +
+𝐶
03
∙
1
𝑥
2
(𝑥
1
2
− 𝑥
4
2
) ∙ (𝑥
3
− 1)
→ 𝑚𝑖𝑛 (13)
To ensure the operability of the structure, the following limiting conditions must be provided. 
1) the condition that electromagnets can turn on the brakes. 
To ensure the span of the brake pads, a solenoid is used, placed in parallel along three axes. The 
condition under which the solenoid can apply the brake will be as follows: 
𝟑𝑭
𝒆𝒍
∙ 𝒌
𝒆𝒍
≥ 𝑭
𝒚
=
𝑻
𝑻
(𝒛 − 𝟏)𝒇𝑹
𝒐𝒓
(𝟏𝟒)
 
or 
𝒈
𝟏
= 𝟑𝑭
𝒆𝒍
∙ 𝒌
𝒆𝒍
−
𝑪
𝟏
(𝒙
𝟏
𝟐
− 𝒙
𝟒
𝟐
)
(𝒙
𝟏
𝟐
− 𝒙
𝟒
𝟐
) ∙ (𝒙
𝟑
− 𝟏)
≥ 𝟎 (𝟏𝟓)
 
where
𝐹
𝑦
=
𝑇
𝑇
(𝑧−1)𝑓𝑅
𝑜𝑟
- 
compression force of the cylindrical central spring;
𝐹
𝑒𝑙
- longitudinal force 
created by the electromagnet; 
𝐶
1
=
3∙10
3
∙𝑇
𝑇
𝑓
;
𝑘
𝑒𝑙
- 
safety factor. 
2) the condition of the rigidity of the brake pulleys. 
Pressure
(𝑝)
on the surface of the brake pads should be less
[𝑝]
, 
than the allowable value for the 
pad material, i.e.: 
𝒑 =
𝟑𝑭
𝒆𝒍
∙ 𝒌
𝒆𝒍
∙ 𝒌
𝟏
∙ 𝒌
𝟐
𝑨
𝟎
≤ [𝒑] (𝟏𝟔)
 
where
𝑘
1
- coefficient taking into account the uneven distribution of the load along the diameter of the pulleys;
𝑘
2
-coefficient taking into account the uneven distribution of the load between the pulleys;
𝐴
0
=
𝜋
4
(𝐷
𝑥
2
−
𝐷
0
2
)
- the area of the working surface of the brake disc. 
Taking into account the expressions 
𝐴
0
in (16), we get: 

---

The XXXVI International Scientific Symposium "Multidisciplinary Studies of the Turkish World" 
The 25
th
 of March 2023 ISBN: 978-605-72481-0-7 Eskishehir / Türkiye 
 
---187--- 
𝒈
𝟐
= [𝒑] − 𝒄
𝟐
∙
𝟏
𝒙
𝟏
𝟐
− 𝒙
𝟒
𝟐
(𝟏𝟕)
 
here 
𝑪
𝟐
=
𝟏𝟐𝑭
𝒆𝒍
∙ 𝒌
𝒆𝒍
∙ 𝒌
𝟏
∙ 𝒌
𝟐
𝝅
 
3) condition of wear resistance of brake pulleys. 
One of the parameters characterizing the basic performance of the brake is its wear resistance. The 
condition of wear resistance of brake pads can be expressed by the formula: 
𝜹
𝒚
= 𝒌
𝒊
(
𝒉
𝑹
)
𝟏
𝟐
∙
𝑷
𝒂
𝒑𝝉
∙
𝟏
𝒏
𝒊
∙ 𝑳 ≤ [𝜹
𝒚
] (𝟏𝟖)
 
here, 
[𝛿
𝑦
]
- the output power of the brake pulleys was assumed to be 
[𝛿
𝑦
] =
1
3
𝛿
1
; 
𝑘
𝑖
- coefficient, depending 
on the geometric shape and 
ℎ
𝑅
-
height of the section of the surface of the brake pads 
𝑘
𝑖
= (0,15 . . . 0,21)
;
- 
ratio of surface stuttering to its average radius
(
ℎ
𝑅
= 10
−1
÷ 10
−2
)
; 
𝑝
𝑎
𝑝
𝜏
- 
the ratio of the nominal pressure on 
the contact surface to the actual pressure
(
𝑝
𝑎
𝑝
𝜏
= 10
−1
÷ 10
−4
)
; 
1
𝑛
𝑖
- 
coefficient characterizing the resistance 
of a material to destruction under repeated exposure 
(
1
𝑛
𝑖
= 10
−1
÷ 10
−12
)
;
𝐿
- 
Whether the friction path is 
found as follows [4]: 
𝑳 = 𝑺𝒏 (𝟏𝟗)
 
here 
𝑆
- is the path of the brake disc during braking, for a uniform deceleration it is found as follows: 
𝑺 = 𝟎, 𝟓𝒗𝒕
𝑻
= 𝟎, 𝟓 ∙ 𝟎, 𝟓 ∙ 𝝎𝑫
𝒙
𝒕
𝑻
=
𝝎𝑫
𝒙
𝒕
𝑻
𝟒