Conference Paper · March 023 citations reads 163 authors

 
𝒏 = 𝑻 ×

(𝟐𝟎)
 
where 
𝑛
- is the number of attachments during the operation of the brake; 
𝑇
- is the running time of the brake 
pulleys per hour. 
Taking into account expressions (19) and (20) in expression (18), we obtain: 
𝜹
𝒚
= 𝒌
𝒊
(
𝒉
𝑹
)
𝟏
𝟐
∙
𝑷
𝒂
𝒑𝝉
∙
𝟏
𝒏
𝒊
∙
𝝎𝑫
𝒙
𝝉𝑻𝒗
𝟒
≤ [𝜹
𝒚
] (𝟐𝟏)
 
Then we can express the condition of resistance to eating as follows [5]. 
𝒈
𝟑
= [𝜹
𝒚
] − 𝑪
𝟑
∙ 𝒙
𝟏
≥ 𝟎 (𝟐𝟐)
 
here 
𝑪
𝟑
= 𝒌
𝒊
(
𝒉
𝑹
)
𝟏
𝟐
∙
𝑷
𝒂
𝒑𝝉
∙
𝟏
𝒏
𝒊
∙
𝝎
𝟒
𝝉𝑻𝒗
 
4. Geometric dependencies of the design are conditional. 
𝒈
𝟒
= 𝒙
𝟒
− 𝑩𝒅
𝒗
≥ 𝟎 (𝟐𝟑)
 
where 
𝑑
𝑣
-
is the diameter of the shaft; 
𝐵 = (3,5)
- 
is accepted. 
𝒈
𝟓
= 𝒙
𝟑
− 𝟑 ≥ 𝟎 (𝟐𝟒)
 
Thus, the task is to find the expression (12) g_0 of the objective function (14), (17), (22), (23) and (24) 
are reduced to finding the minimum under the restriction conditions. The compiled optimization problem 
belongs to a non-linear programming model. To solve problems of this type, a very common penalty function 
method is used. In this method, we determine the minimum of the function (12) and (14), (17), (22), (23) and 
in order to find the optimal values of the parameters x_i that ensure the satisfaction of (24) of the constraint 
conditions, we bring the problem to finding the unconditional minimum of the penalty function with successive 
approximation. To do this, we formulate the penalty function as follows. 
𝑭(𝑿
𝒖
) = 𝒈
𝟎
(𝑿
𝒊
) + 𝒓 ∑
𝟏
𝒈
𝒋
(𝑿
𝒊
)
𝟓
𝒋−𝟏
(𝟐𝟓)
 
where 
𝑟
- is the penalty factor;
𝑔
0
(𝑋
𝑖
)
– objective function,
𝑔
𝑗
(𝑋
𝑖
)
- limit functions. To find the minimum 
of function (25), a special program was developed, the implementation of which was carried out on modern 
computers. The optimization of a multi-disc friction brake used on hoisting machines was carried out based 
on the following input data: 
𝑇
𝑇
= 93,3 𝑁𝑚
; 
w
= 76,4 𝑟𝑎𝑑 𝑠𝑎𝑛
⁄
; 

= 120 1 𝑠𝑎𝑎𝑡
⁄
;

= 0,3
; 

---