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????????? ????????????? ???????? ???????????? ???????????????????????? ?????????? ???? ? ???????? ????????? ??? ???????? ?? ????????? ?????

?????????? ????????? ???? ????? ????????????? ???? ???????? ???? ? ????? ????????????? ??? ????? ???? ??????????? ???? ? ?????????? ???????? ????????????, ???? ? ?????????? ?????????????? ?????? ?????? ? ????? ????? ?????????????. ? ?????? ?????? ????????? ???????? ???????? ?????? ? ????????????? ? ??????????? ? ?????. ?? ?????? ?????? ? ?????????????? ????? ??????? ??????????? ?????????, ????? ??????? ?????? ???????? ??? ??????? ????????? ? ?????.

???? ?????????????? ???? ???????? ? ??????????? ??????? ?????????????? ?????? ?????? ? ?????, ?? ????? ????? ???????????????? ??????? ???????????? ? ????????? ???????, ??????? ????? ???? ?????????? ????? ??????? ?????????? ?????? ?????? ?????????. ? ?????? ????? ??????????, ? ??????? ????????? ??????????????? ???? ??????, ??????????? ?????????????? ??? ???????? ? ????????, ? ??? ???????????? ???????? ????? ???? ??????????? ????????? ????.

? ????????? ????? ??????? ???????????? ?????????? ???? ??? ???????? ?? ????????? ????? ???? ??????????. ?????? ? ??? ?????? ? ??????? ????? ? ???????? ???????? ????? ?????????? ??????? ????? ? ?????????. ????? ????, ??????? ????? ?????? ??????????? ????? ?????? ?????????? ????? ? ??????? ????? ? ????????. ??? ????????? ?? ??, ??? ?????? ?????? ???? ????? ??????? ???????????? ???????.

? ?????????? ??????? ????????? ????????? ?????????? ???????????? ???????????????? ????????. ? ?????? [1] ????????? ????????????????? ???????????? ???????? ???????????? ?????????? ???? ??? ???????? ???????????? ????????? ?????? ?? ???????? ????????? ?????????? ??????????? ??????????? ?????. ????? ?????? ????? ?????? ???????????? ? ??????? ????????? ? ?? ????????? 1000 ????????? ????? ?????? ? ???????. ? ?????? ????????, ??? ????? ?????????? ????????, ??????????? ????????? ????????? ???????? ?????, ??????? ???????????????? ?? ??????????? ???????? ???????????? ? ????? ?????????? ??????.

???? ????????? ?????????????? ?????? ???????? ???????????? ??? ?????????? ???? ????? ???????? ??????????, ??????? ???????? ????????? ? ????? ?????? ?? ????????? ????? [2]. ?????? ???????????? ?????????? ???? ??????? ???????? ?? ??? ???????: ???????, ? ??????? ????? ???? ???????????? ????????????????? ?????? ??????, ?????????? ??????? ? ??????? ?????? ????????. ? ??????? ???????????? ????????????????? ?????? ?????? ????????? ???????? ????????????? ????????? ???????????? ?????????. ???????????? ?????? ?? ?????????? ?????? ?????????? ???????. ??? ??????????? ????? ??????? ?????????? ?????????? ?????????????? ?????? ???????? ?????????? ????????? ? ?????????? ???????. ????? ??????????????, ??? ? ?????????? ??????? ????????? ???????? ????? ???? ??? ??????? ??????????? ????.

????????? ?????????? ???????? ??? ?????????? ?????????, ??????? ????????????? ? ????????????? ? ?????? [1]. ??? ???? ???????? ?? ???????? ??????????? ?????, ????? ?????? ???????? ?????????? ?????? ???????? ????????? ???? ?????? ? ???????? ?????????? ?????? ???????? ??? ? ????????????. ?????????? ???????? ????????? ? ?? ?? ??????? ???????, ??? ? ? ?????? [1]. ??????? ?????????? ??????????? ??????? ??? ????????? ???????? ??????? ?????????? ??????? ? ????????????????? ??????????? ???????????? ??????????? ???????????? ?????? ???????????????? ???????? ??? ?????? ???????. ? ?????? ??????? ?????????? ??? ??????? ?? ??????????? ????????? ????? ?????? ????????????? ?????? ?????????? ?????????.

1. ?????????? ??????. ????? ?? ??????? ??????? ???????? ????????, ??????? ???? ? ????? ????? ? ???????????? ? ???????, ?????? ??????? ???????????? ?? ?????? ?????. ???????? ??? ????? ????? ??????????? ? ????????? ? ????? ?? ????????. ???? - ???????? ?????? ???????? ???????? ???, ?? ??????? ??? ?? ??????? ??????? ?????????????? ?? ??????? .

????? ? ?????? ??????? ???????? ???????? ?????????????? ?????????, ?????? ???????? ???????????? ? ????? ???????? ?????????? ? ???? ???????. ???????? ????????? ?????????????? ?? ??? ???, ???? ???????? ???????? ??????? ???????????? ?? ?????? ???????? . ????? ????? ??????? ??????? ???????? ????????? ??????????, ? ???????? ???????? ??????? ???????????? ????? .

? ???????? ?????????????? ??????????? ??? ??????? ??????????? ???????? ???????????? ? ??????? ???????? ???.

????? ???????? ???????? ?????????, ????????? ???????? ?????????? ??????????? ????????????? ? ?????????? ?????, ? ??????? ? ????????? ????????? ????????? ?????????? ????????, ??????????? ?????????? ?????????? ???????? ????????? ???? ?? ????? ? ??????????? ????? , ??????? ?????? ???????? ??? ???????? ???????????. ????????? ?????????? ????????? ????? ????? ???????? ?????? ???????? ? ????????, ?????????? ????????? ?????, ? - ?????????? ?????? (????????) ????????? ????? ??????? ?????? ???????? ??? (???.3.1).

? ????????? ?????? ???????, ????????, . ? ??????? ???????? ???????????? ????? ?????????? ??????, ? ??????? ??????????? ????????? ??????????. ? ??????????? ???? ????????? ??????? ???????? ??????? ??????? ?????? ???????? ??? ???????? ????????? ??????? ????????? ????? ??????? ?????? ????????. ???. 3.1 ????????? ? ?????? ??????? ?????.

Fig1

???. 3.1

???????????? ??????? ?????????, ??????????? ?????? ??????? ?? ???????, ????? ??????????? ????????? ???????? ???? ?????. ????? ????, ??? ?????????? ?????????? ???????????? ????????? ?????, ?????? ??????????? ?????????? ??? ???????? ????? ???? ?????? ???????, ??????????, ????????, ? [3].

????????, ??? ? ??????? ????? ??????? ??????? ?????????? ????????? ? ??????? ??????? ??????????? ??????? ???????????? ????????????????? ?????? ??????. ?????? ? ??????????? ????? ??? ??????? ??????????. ????? ????, ??? ??? ? ??????????? ????? ??????? ?????????? ???? ????, ?? ????????????? ???????? ?????????? ????????? ?????????? ?? ??? ???????? ????????????? ???????. ??? ????????????? ???????? ?????????? ????????? ??????????. ? ????? ? ???? ???????, ??????????? ????????? ??????????, ???????? ?? ??? ?????.

????????, ??? ? ?????? ?????, ???????????? ????????? ?????? ? ??????????? ? ?????? ? ??????????? ??????????? , ??????????? ??????? ???????????? ????????????????? ?????? ??????. ?? ?????? ?????, ???????????? ??????? ? , ????????? ???????? ?????????? ????????? ??????????. ????????? ????????? ? ???, ??? ?????? ??????? ?? ???????? ?? ????????, ?. ?. , ? ??? ? ???? ??????? ????????? ???????? ???????? ??? ??????? ??????????? ????. ? ?????? ?????? ????????? ????????? ??? ??????? ?????????? ???? ? ???? ??????? ????? ??????????? ? ????

, (3.1)

??? - ???????? ???????? ??????? ????? ???????? ?????? ???????? ? ???????? ???????????? ????????. ???????????????? ????????? (3.1) ???????? ?????? ?? ????????? . ????? ?????????????, ??? ??? ??????? ?? ????????? (28), ??????? ???????? ??????????. ?? ????? ???????, ??? ????????? (28) ????????????? ????????? ???????? ?????????? ????????? ?? ????????? ??? ???????? ???????? ???????????? ????.

???????, ??? ? ??????? [4,5] ? ??????????? ??????? ?????? ????????? (3.1) ?????????????? ?????????

(3.2)

??? - ???????? ??????? ???????????? ?????????. ???????? ????????? (3.2) ???????? ???????? ?????????? ????????? ? ????????? ??????????? ????? ??? ???????? ???????? ???????????? ???? ?? ????????? . ??????, ???????? ???????? ?????????? ????????? ? ??????????? ????? ?????? ????????? ?? ????????? ???????? ????? ????? , ?? ???? ??????? (3.2) ???????? ????? ?????? ?? ????????? ? ???????? (3.2).

????? ???????, ??? ??????? ??? , ? ??????? ?????? ??????? ? ?????? ??????? , ????????? ?? ??? ??????? (???. 3.1). ? ?????? ???????, ??????? ???????????????? ?? ??????? ????????? ????? ?????????? ???? (????? ?? ???. 3.1) ?? ????? , ??????? ????????????? ????????????? ????????????????? ?????? ??????. ? ?????? ????? ????????????? ???????? ? ??????? ???????????? ?? ????????? ?????????? (17), ??????? ? ??????????????? ?????? ????????? ???

, , (3.3)

??? - ????????? ????????????, - ??????? ?????????? ????; - ????????, ??????????? ? ????????? ????, - ???????? ? ????????? ?????????? ????????? ??????????????.

?? ?????? ???????, ??????? ???????????????? ?? ????? ?? ????? , ?????????? ????????? (3.1). ? ??????? ???????, ??????? ???????????????? ?? ????? ?? ???????? ????????? ????? ??????? ????????, ?????????????? ????? ??????? ???. ??????? ???????? ??? ?? ??????? ??? ???? ????? ???????? ? ????

, . (3.4)

? ????? ????? ????? ????????? (3.4) ????? ????, ??????? ??? ??????????? ???????? ??? ?????????? ????????? ????????? ???? ????? ????? (3.4) ? ???????.

????? ????? ????????????? ?? ??????? ????? ??????????? ????????? ???????

, . (3.5)

??? ????????? (3.3) ?????????? ?????? ????????? ???????. ?? ??????? ??????? ??????? ?????? ? ??????? ????

. (3.6)

?? ???????? ??????? ??????? ?????????????????? ??????? ?????????? ????????? ? ???????? ?????????? ??????? ?????? ??????? ????????????? ????????, ?. ?.

.

????? ????? ?????????, ????? ??????? ???? ??????????? ? ????????? ????? ??????? ?????? ????????, ?. ?.

.

??????? ????????? ???? ???????? ? ????????? ????? ??????? ?????? ???????? ????????? ?? ???????, ??? ??? ??? ??????? ????? ??????????? ?????????????. ??? ??????? ?? (3.4), ??? ??? ???????? ? (3.4) ????? ?????????? ? ???? ??? ?????? ? ??? ??????, ???? ??? . ????? ????, ????????? ????????????? ?????? ?????????? ?????????

?? ??????? ????? ????????? 1 ? 2, ?. ? ????????? ?????????? ???????

. (3.7)

? ????????? ?????? ??????? ?????????????? ????? ??????? ??? ?? ??????? ,

??? - ???????? ?????? ??????? ???????? ??? ????? ???????? ???. ????? ???????, ????????? ??????? ?????? ????? ???

? ??????? ,

? ??????? . (3.8)

????????, ??????????? ? ???????, ?????????? ????????? ?????, ? ? ??????? ?????? ????????, ?????????????? ??????????? ? ?????????

????????, ?. ?.

. (3.9)

??? ????????, ?????????? ? ??????? ????? ?????????.

???? ??????? ? , ? ????? ???????? ??????? ?????????? ? ??????????? ????????? ? ???????? ??????, ?? ??? ????????? ? ??????? ?????????? ??????? ? ????????? , ? ????? ??????? ? ??????? , (???. 3.1). ?????????????, ????? ????? ?????? ? ??????? (2) ????????. ? ??????

, ,

??? ????? ? ??????? ?????? ??????? ???????????? ?? ??????? (3.8). ? ?????? ????? ????????? (3.4) ????????? ? ?????????? (3.5) ????? ????????????? ??? ???? ???????????? ????????? ???????????? ? ??????? . ???? ?? ??????? ? ???? ????????, ??, ????? ??? ???????????? ?????????, ????? ???? ?? ?????????? ??????? ? ??????? . ????? ?????, ????????? ?????????? ???????? ??????? ? ????? ??? ????????? ??????? ??? ????????? ??????????, ????? ???? ??, ????? ??? ?????? ? ??????? 1, ?????????? ? ???? ??????? ??????? ? . ????? ??????? ????? ??? ????????? ???????? ? ?????????? ??????? ? ?? ???? ???????? ??????. ?????? ??????? ? ??????????, ?? ??? ?? ??????????? ??????? ??????? (3.7) ? (3.9). ?? ???? ??? ??????? ?????????? ????????? ??????, ????? ??????????? ??????? (3.7) ? (3.9).

? ?????????? ????? ??????? ??????? ?????? ???????? ? ????????? ????, ??????? ?????????? ???? ? ????? ?????????? ????????? ????? ???????????? ????????? ? ???????, ???????????? ??? ??? ??????????????? ???????.

????? ??????? ????????? ???????? ????????? ?????? ?????????, ???????? ??????? ??????? ?? ????????. ??? ????? ????????? ???????? ???????? ? ?????????? ???????? ?????????? ?????? ???????. ??????????? ????????? ?????????? ????????? ?? ???????? ?????? ? ???? (17), ? ??????????? ???????? ?? ???????? ? ???? (19).

2. ?????? ???????????. ?? ?????????? ????? ???? ????????? ??????? ???????? ?????????? ????????? ? ?????????????? ?????? ??? ??????????????? ???????? ????????? ?? ????????? ?????. ????????? ??? ???????? ?????????? ??????, ??? ??????? ? ???????? ???? ??????????? ?????? ? ???????? ? ????????????????? ?????????????, ?????????????? ? [1].

??? ????? ??? ?????? ???????????, ??????????? ? [1] ?? ??????? HVI 650 ??? ?????? ???????, ??????????? 80 ? ? ????????? . ? ?????? [1] ????????????? ??????? ? ?????????? ????????? ?????? ?? ???????? ????? ??????? ????????? ??????? ??????????? ?????. ??????????? ???? ????????? ????? ???? ????????? ??? ????????????? ??????? ???????? ???????? ?? ??????? ??????????? ??????? ???????? ????.

? ????? ??????????? ????????? ? ????????????????? ??????? ? ???????? ??? ??????? ???????? ???????????? ??????? ? ???????? ?????????? ??????, ????? ??????????? ??? ???????. ?????? ??????? ??????? ? ???, ????? ? ????????? ?????? ??????? ?????? ????????? ???????? ???????? ? ?????????????? ???????? ?????? ????????? ???????? ???????? ???????? ? ???????? ???? ? ??????? ????????????, ??????????? ? ????????????. ?????? ??????? ??????? ? ???, ????? ? ???????????? ?????? ??? ?????? ??? ???????? ??????? ????????????? ? ????????????????? ??????? ?????????? ???? ? ??????? ???????? ???????? ?????????. ???????? ????????? ?????????? ??????????? ?????? ??, ?????? ??? ????????? ? ?????? [2]. ? ?????????? ??? ???????? ???????????? ????????? ???????? ??????????: m0 = 0.052 ???, a = 1.96108 ??1, g = 10 ?/?2, R = 0.0093 ?, u0 = 0.2 ?/?, E = 1.191011 ??, pg = 0.4 ???. ???????? ?????????? p0, C1, C2 ? ?????? [9] ?? ?????????. ??? ??????????? ??????????: 1/p0 = 5.1109 ??1, C1 = 0.6109 ??1, C2 = 1.7109 ??1, ??? ????????????? ????????? ? ?????????? ?????? [1]

???????? ????????? ??????????? . ???? ????????? ?????????? ???????? ??? ???????? ????????? .

?? ???. 3.2 ????????? ??????????? ??????? ?????????? ???? ?? ?????????? x ? ????????? ??????? ???????. ?????????? ??????? ???????????? ?? ??? ? ???? ?????? ????????? ????????. ??????? ??????????, ??? ??? ??????? ???????? ???????? ??????????????? ?????? ????, ?. ?. ??????????? ??????? ????????? ???? ?? ?????. ?????? ????? ????????? ????? ????? ??????? ?????????? ???????????? ??????? ?????????? ???? ??????????? ?? ??????? ?? ???????? ????????? .

?? ???. 3.3 ????????? ??????? ????????????? ????????????? ???????? ? ????????? ??????? ???????. ????? ????????? ????? ????? ?????? ???????? ???????? ?? ??????? ????? ?????????? ???????? ? ????????, ? ??????? ???????????? ????????? ????????????????? ?????? ??????, ??????????? ??? ????????. ?????, ??? ?? ???? ??????? ??????????? ???????? dp/dx ?????? ??????. ??? ???????? ?????????? ????, ??? ?? ?????? ??????? ??????? ???????? ?????? ??????????? ??????? ????????, ?????? ??? ???????? ?? ??????? ???????? ?????????????.

? ??????, ? ??????? ???????? ?????? ??? ???????? ?? ??????? ???????????? ???-?????? ?????? ? ?????????? ??????? ????? ???????? ??????????, ??????????? ???????? ?? ?? ??????? ????? ????? ???????????. ? ?????????? ??????? ???????? ??????, ?????? ?? ??????? ????? ?????????? ???????? ? ???????? ?????? ???????? ??? ????? ?????????? ??? ????????, ?? ?? ????????? ????.

???. 3.2

???. 3.3


????? ???????? ?????????? ???????? ???????????? ? ???? ???? ???????????? ????????

??????? ?????????? ???????????? ? ?????????? ?????? ????????? ?????????? ??? ???????? ?? ????????? ????? ????????????? ????????? ???????????? ??????:


???????? ????????? ??????????? ???????? ?? ???????? ??? ???????????? ?????????? ???? ??? ???????? ?? ????????? ????? ????????????? ????????? ???????????? ??????:


???????????? ?????????, ??????? ???????????? ?????? ??????????, ?????????? 20 ???????????. ? ?????? ??? ???????????? ??????? ???????? ???????? ??????????? ??? ?????????. ??? ???? ???????? ?? ??????? ??????? ?????????? ???????????. ? ?????? ????????? ????? ?????? ???????? ???????????? ???? ???????? ?????????? ?????????? ???????????? ?? ??????? ???????. ??? ???? ????? ?????????? ????????? ????????? ?????????????? ??????????? ???????? ????????????. ????? ??????????? ?????? ?????????? ????????? ? ??????????? ???????? ???????????? ?? ??????? ??????? ?? ??? ?????? ???????????, ? ???? ???????? ?????????? ????????? ??????.

? ?????? ??????? ?????????? ?????? ?????????? ???????????? ????????? ??????????. ????? ?????????? ???????? ???????????? ???? ?? ????? ?? ???????? ??????? ?????????? ????, ??????? ??? ????? ? ???????????? ??????.

?? ???. 3.4 ????????? ??????????? ???????? ??????? ???????????? (?????? 1) ? ???????? (?????? 2) ?? ??????? ?? ??????? ???????????? ???????????? ???? ?? ?????. ?? ??????? ?????, ??? ???????? , ??????? ????? ????? ??????? ????????? ???????? ?????? ?????????? ?????????, ? ????????? ?????? ??????? ??????????? ???? ???????? . ? ?????????? ???????? ?????????? ?? ????????, ???????? , ?? ???? ?????? ??????? ???????? ???? ???????? .

Fig3

???. 3.4

?? ???. 3.5 ????????? ??????????? ????????? ????????? ????? ??????? ?????? ???????? (?????? 1) ? (?????? 2) ?? ???????. ?????, ??? ????????? ????? ???????? ????????? ???? ?????, ??????, ???? ????????? ????? ???????? ??????, ?? ????????? ????? ???????? ????????.

Fig4

???. 3.5


??????????

1. Glovena R. P., Spikes H. A. Elastohydrodynamic film formation at the start-up of the motion.- Proc. of I. Mech. E. Part J. J. of Eng. Tribology, 2001 (215), N 23, 125138

2. ???? ?. ?. ????????? ?????? ???????? ???????????? ???????????????????????? ?????????? ???? ? ???????? ????????? ??? ???????? ?? ????????? ?????.-?????? ? ?????, 2008 (29), ?1, ???. 69-82

3. ???? ?.?. ? ???????? ?????????? ??????? ???-?????.-?????? ? ?????,2006(27), ?4, ???. 394-402

4. Osborn K. F., Sadeghi F. Time dependent line EHD lubrication using multigrid/multilevel technique.- Trans. ASME. J. of Tribology, 1992 (114), 6874

5. Mongkolwongrojn M., Thammakosol K. Theoretical investigation of transient elastohydrodynamic lubrication with Newtonian solid-liquid lubricants,- Lubrication Science, 2005 (17), N 3, 347357

 

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