Latvian Maritime academy
Latvian Maritime academy
Latvian Maritime academy
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Let be the distance from the considered contact point N of roll with coating till the vertical line<br />
which passes through axis of roll and the maximum contact point A . Then sediment of coating in the<br />
considered contact point M is presented by formula analogous to the formula (4), but with the<br />
substitution a to and hn1<br />
to x :<br />
2<br />
2R(<br />
h n x)<br />
we shall find<br />
2<br />
<br />
x hn<br />
<br />
(5)<br />
2R<br />
Differentiating (5) by time t and taking into consideration that<br />
d(<br />
R )<br />
d<br />
<br />
dt dt<br />
we shall obtain<br />
dx <br />
(6)<br />
dt R<br />
We shall put this expression into (2), and find:<br />
<br />
m <br />
HR<br />
(7)<br />
Necessary force P , pressing the roll to the coating is determined as a sum of contact reinforcement under<br />
the roll:<br />
a<br />
P <br />
bd<br />
. (8)<br />
Where b is the width of thin border of roll. Taking into consideration (7) in (8) for this force we shall<br />
find the expression:<br />
a<br />
<br />
P ba<br />
m . (9)<br />
2HR<br />
<br />
This formula at this compressed force of roll P , determines the length a of contact of roll with coating.<br />
Knowing this quantity, from (4), according to ratio:<br />
2<br />
a<br />
h h <br />
. (10)<br />
n<br />
0<br />
n 1 <br />
2R<br />
Sediment on the next n on numbers of rolling is found. From formula (10) it results that the most quantity<br />
a of section length of contact corresponds to the most compression of coating. From (9) we have<br />
<br />
<br />
mHR<br />
2vP<br />
a 1<br />
1<br />
2 . (11)<br />
<br />
bHR<br />
m <br />
According to this formula the least velocity corresponds to most quantity a . We shall get from (9) the<br />
limit value of maximum quantity a , when 0<br />
max<br />
P<br />
amax . (12)<br />
b<br />
And then in accordance with the ratio (3) and (4) we shall get the joint of coating sediment for maximum<br />
quantity:<br />
2<br />
2<br />
amax<br />
P<br />
hmax<br />
. (13)<br />
2 2<br />
2R<br />
2Rb<br />
m<br />
At greater value of velocity , emitting the first item of the right of formula (9) we shall get<br />
b b<br />
P a 2 <br />
h<br />
. (14)<br />
2HR<br />
H<br />
Whence we shall get<br />
m<br />
6