Modelling forces and stresses of strip steel in a galvanising bath (modelled as a of pulley) 1

[RhysF]

Hello,

Firstly I would just like to say hello to the community here, as this is my first post. I've been looking to join technical discussion board for a while.

I am currently writing a research thesis on the design of bearings inside a galvanising bath. I want to work out the forces on the bearings so I can calculate the stresses inside them and decide if I have used enough material to withstand the stresses.

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The galvanising bath is comprised of one main roller (2150mm * 800mm), in which the strip steel enters at an angle 27.5 degrees in the second quadrant of the vertical axis. After the strip steel has passed around the main roller (called '1' in the schematic), it passes around two 'stability' rollers (2150mm * 200mm), entering the first stability roller at an angle of 13.175 to the vertical axis in the second (negative y) quadrant, and then is goes back at an angle of 22.964 degrees to the vertical axis in the first (positive y) quadrant. Please see the attached link for a schematic of the problem. After it passes through the second stability roller it moves vertically up along the y axis.

The strip steel is of thickness 2mm, and 1800mm wide, assume constant length. The strip is under 40KN of tension, and the strip moves at 160m/min.

So my problem is, how can I work out the distribution of forces across the rollers based on 40KN of tension? I imagine between the 3 rollers (1 main and 2 stability rollers), they will each have 40KN of tension force distributed between, but how can I split this up between the 3 rollers? Because the strip steel behaves like a pulley I have decided to model it based on a pulley system with the strip steel becoming a belt.

I have imagined a few ways I can calculate the forces. The first is way is simply to take simple free body diagrams of each rollers but I am confused as to how I can accurately split up the 40KN of force between the 3 rollers.

So, what I need is to calculate how the 40KN tension force of the steel strip (or pulley belt) is applied to each of the rollers and then how that force translate to the bearings which are located on the end of the rollers.

I appreciate any feedback you may have and can provide any additional information you may need.

 

[3DDave]

The only way for the load to change on the rollers from 40kN is if there is a torque applied by a roller.

If not, then each roller is on its own.

 

[tbuelna]

This is actually quite an interesting problem, due to the effect of the bending stiffness in the 2mm steel sheet. The 2mm thick steel strip will likely yield as it tries to wrap around the 400mm radius of roller no.1 under 40kN tension, but what effect will this have on the radial forces produced on rollers 2 & 3 as it is forced to bend in the opposite direction?