Wire rope and pulley sheave resistance calculation

[Alan Goodchild]

Hi, this is my first posting on this forum in the hope someone could assist me with a calculation.

I have read several threads which I think partly covers my problem but to be honest the example answers given are way beyond my comprehension.

Basically I need to raise a platform which runs on two vertical tracks by the use of stainless steel wire rope which runs over and around a series of sheaves to a hydraulic ram. Space dictates the maximum ram stroke I can accommodate is 600mm and I need a vertical lift of 2m. The total load including the platform is 430Kg so I have come up with a workable solution based upon an earlier unit I built. Although this only had one sheave so the calculation was within my scope with a bit of guesswork for resistance.

I have tried to find out the resistance of the pulley sheaves which are 75mm dia. from the supplier, but they are rather vague and suggest I allow between 5 - 10% on top? However, reading some earlier threads I have seen one reference for plain bearing sheaves, K = 1.09.

I am attaching a diagram which I hope explains the principal of this design, if anyone is able to assist in plain English what push the ram (in Kg) is needed it would be extremely helpful.

Many thanks in advance.

 

[SteamKing]

I think the interpretation of K is this: suppose you have a single sheave, which suspends a load W. If this were a frictionless sheave, then the force F required to move the load would be F = W. However, to overcome friction is a sheave which has a K value of 1.09, then the force required to move the load would be F = K*W = 1.09 W.

 

[Alan Goodchild]

Hi, I sort of understand that if the value of K is 1.09 I need to add 9% to the weight being lifted, but what confuses me is if you look at my diagram there are 10 sheaves on the lift wire to achieve the required lift with a ram stroke of 600mm. Therefore does the increase of 9% apply to every sheave in the system as a compound increase or am I missing something. Clearly my ultimate aim is to to specify a ram with sufficient output force to cope with the raising of 430Kg.

Any help in showing me how to calculate this would be much appreciated and thanks for your reply.

 

[SteamKing]

Yes, every sheave will experience a frictional loss.

 

[Alan Goodchild]

Okay, if you could please clarify how I approach the calculation: Do I simply multiply 215 x 1.09 (19.35) and multiply the answer by10 which is then added to the 215, or does the 215 x 1.09 = 234.35 then have the multiplier of 1.09 added again (255.4415) and continue this for 10 times to arrive at the final force?

Sorry being really thick here but have researched so much now even the answers are confusing me!

 

[etudiant]

Each sheaf 'sees' the force as an input and you need to multiply that by 1.09 (pretty good sheaf incidentally) to account for the sheaf losses.
So overall, if you have 10 sheaves in the system, the end to end force needed to lift the load and account for the losses will be the load times 1.09**10, or load times 2.36736, according to Wolfram.
You might reasonably think about using a factor of 5, just to leave a margin of safety in your setup.