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Help with rollers lifting an object
I'm trying to design a hydraulic system that that will lift a tire on a car off the ground with a fixed roller and a sliding (laterally) roller driven by a hydraulic cylinder. In the picture below is a basic layout of what is going on. The black circle is the tire and the two blue circles are roller tubes. Before I determine the pressure of my system, pump speeds, HP, etc I want to find out how much force will be required to lift the tire (one corner of the car) but since the rollers will rotate about its axis, I think I might get a mechanical advantage so my hydraulic system won't have to work as hard.
Black tire = we'll say it weighs 2000 lbs and can only move up and down (27" diameter)
Blue circle (1) = 1.5" roller that is fixed to the machine but it can rotate about its axis (looks like it will rotate CCW)
Blue circle (2) = same 1.5" roller but it slides laterally (left to right) by means of a hydraulic cylinder. It too can rotate about its axis (rotate CW)
F = The force applied to the sliding roller tube that is pushing in the direction towards the other roller (#1)
The center of the rollers are about 1.25" off the ground and the tire is on the ground. For now I'm assuming that the tire is not deforming while it is on the ground and also the tire will not deform when the rollers engage the tire.
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What I am trying to determine is the equation that takes into account the fact that those rollers will be spinning (outward) as roller #2 moves inward and begins to lift the tire.
I started my design by taking a 1500 PSI system and a 1.5" bore cylinder and I calculated that I could produce about 2650lbs of force which seemed like I was where I wanted to be. But then I was thinking about how those rollers with respect to the tires should be making it easier to lift with each millimeter more a lateral travel. Is there an equation that I can put in the tangent relationship between the rollers and the tire with a given force applied?