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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

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