Разработка ионно-плазменной технологической установки для нанесения функционального покрытия на крышки масляных фильтров, страница 26

On the anode-collector thermal stresses ( К) act. Acting loadings are shown in figure 3.4.

Figure 3.4. The scheme of loadings acting on the anode-collector.

For definition of the stresses arising under action of temperatures difference, we shall determine the flexure of the anode from acting loadings, solving the equation:

 ,                                                           (3.24)

where E=1.98·10⁵ MP – Jung's module, μ=0.25 – Poisson factor, 1/К – linear expansion coefficient, D – cylindrical rigidity,  m – internal radius of the anode,  m.

,

,

, где .

On a bearing there is crosscutting force. It is necessary to find reaction of the bearing . It will be defined from the common solution of the equation (3.24). Factors  also  are determined from boundary conditions:

1) : :

.

In this case

,

.

2) :

.

Thus, the decision of the equation (3.24) looks like:

.                                  (3.25)

For a finding of stresses  and  we shall write down an elastic component of flexure, and also its first and second derivative:

 ,                                           (3.26)

,                                   (3.27)

.                                              (3.28)

Stresses in the anode-collector we shall calculate under formulas:

 ,                                 (3.29)

,                              (3.30)

.                                              (3.31)

Cylindrical rigidity is defined under the formula:

.                                                        (3.31)

Having substituted the calculated values in formulas (3.29-3.31) we shall receive functions of stress change in the anode-collector on distance from an axial line up to considered section. Calculations are performed by means of program Excel, the received results are presented in table 3.1. Graphs of dependences are presented in figure 3.5.

Table 3.1. Dependence of stress value in the anode on radius of considered section

X, m	, P	, P	, P
0	-6,65E+08	0,00E+00	0,00E+00
0,003	-4,91E+08	1,62E+08	4,04E+07
0,006	-3,36E+08	2,39E+08	5,97E+07
0,006	-2,08E+08	2,58E+08	6,45E+07
0,012	-1,10E+08	2,41E+08	6,02E+07
0,015	-4,10E+07	2,05E+08	5,12E+07
0,018	4,14E+06	1,61E+08	4,03E+07
0,021	3,01E+07	1,18E+08	2,95E+07
0,024	4,21E+07	7,99E+07	2,00E+07
0,027	4,45E+07	4,88E+07	1,22E+07
0,03	4,11E+07	2,52E+07	6,30E+06
0,033	3,46E+07	8,65E+06	2,16E+06
0,036	2,70E+07	-2,00E+06	-5,01E+05
0,039	1,96E+07	-8,03E+06	-2,01E+06
0,042	1,31E+07	-1,07E+07	-2,67E+06
0,045	7,89E+06	-1,11E+07	-2,77E+06
0,048	3,97E+06	-1,01E+07	-2,53E+06
0,051	1,23E+06	-8,43E+06	-2,11E+06
0,054	-5,03E+05	-6,52E+06	-1,63E+06
0,057	-1,47E+06	-4,70E+06	-1,17E+06
0,058	-1,65E+06	-4,14E+06	-1,03E+06

Figure 4.9. The graph of stresses dependences from acting loadings on radius of considered section: 1 - ; 2 - , 3 - .