A 1000 mm wide steel sheet made of C35 is normalized by cold rolling 10 mm thick deformed to 5 mm. The rollers, 600 mm in diameter, run at a peripheral speed of 0.12 m/s.
The deformation efficiency is 55%.
Find out:
a) the roller force
b) the roller torque
c) the performance on the pair of rollers.

a. 20.265 MN

b. 0.555 MNm

c. 403.44 KW

Explanation:

Given:-

- The width ( w ) = 1000 mm

- Original thickness ( to ) = 10 mm

- Final thickness ( t ) = 5 mm

- The radius of the rollers ( R ) = 600 mm

- The peripheral speed of the roller ( v ) = 0.12

- Deformation efficiency ( ε ) = 55%

Find:-

a) the roller force ( F )

b) the roller torque ( T )

c) the performance on the pair of rollers. ( P )

Solution:-

- The process of flat rolling entails a pair of compressive forces ( F ) exerted by the rollers on the steel sheet that permanently deforms.

- The permanent deformation of sheet metal is seen as reduced thickness.

- We will assume that the compressive force ( F ) acts normal to the point of contact between rollers and metal sheet.

- The roll force ( F ) is defined as:

Where,

                     L: The projected length of strip under compression

                     Y_avg: The yielding stress of the material = 370 MPa

- The projected length of strip under compression is approximated by the following relation:

- The Roll force ( F ) can be determined as follows:

- The roll torque ( T ) is given by the following relation as follows:

- The rotational speed of the rollers ( N ) is determined by the following procedure:

- The power consumed by the pair of rollers ( P ) is given by: