Calculation of Load on Centre Idler Roll

[Volantis]

Hi All,

Recently moving from the O&G industry into mining, so I have never done any calcs on conveyors / idlers.

I require some help with calculating the load on a centre roll of a suspended, 3 roll idler set. Doing some research, I find that using catenary action on a cable might be the best approach to doing this, but I have never attempted one before so would like some confirmation and guidance on doing so within this particular application.

Below are some assumptions and numbers that I will use, let me know if there are any other unknown variables that I require.

Assumptions:
70% of total load on the centre roll
Friction = 0.9
Idlers have 45 deg trough angle

Some numbers I have:
belt running at fully loaded case: Q = 15,000 tph
Belt speed: v = 5.5 m/s
Belt tension: T = 520kN
Belt Mass: M = 80 kg/m
Belt width: W = 1800 mm
Material density = 1800 kg/m3

Distances between Suspended (Idler1) and inline (Idler2):
Vertical: Z = 0.382 m
Horizontal: Y = 3.798 m


If someone could help me out / point me in the right direction, that would be greatly appreciated.

Thank yo

 

[desertfox]

Hi

A sketch of the problem would go a long way for us to help you

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[MintJulep]

Twice the tension times some trig function of the angle of wrap.

 

[Compositepro]

Why are you assuming 70%? The center roller should be supporting half the weight between the outer two rollers. Belt tension affects belt sag but not the load on the center idler.

 

[Volantis]

See snapshot of model above. Cannot really provide much more at the moment.

Essentially I need to find the load on the centre roller on the left hand suspended idler. Can see there is a lot of free belt between the suspended idlers and the shuttling idler on the right.

I believe i'll need to calculate the suspended belt length first, and then calculate the forces on the idlers.

Compositepro - Regarding load sharing and distribution on the rollers, idler manufacturer suggests using 70% on the centre roll as a conservative approach.

Thanks

 

[dvd]

Is this a horizontally-curved conveyor?

Either way, there are probably better forums to ask on -

https://forum.bulk-online.com/

You may want to investigate Belt Analyst from Overland Conveyor Company.

Also, it seems like a conversation with an idler manufacturer would be beneficial.

 

[Volantis]

My initial problem starts with finding the suspended length of the conveyor belt (lets treat it as a cable between supports)

Taking an Assymetrical catenary approach (Since the idlers, or in this case considered as simple supports, are at different heights) to the problem.

I've looked at many videos and resources on finding the suspended length, however each example resource requires sag in belt/cable to find length, or length to find sag. Therefore I'm in a loop of what to do.

See below small sketch of the problem and the FBD. I need to calculate the suspended length of the cable/belt. Once I do that I believe I need to find the forces at the supports (idlers) and hence the centre roller?

Help is greatly appreciated.

Thanks