Ok, I make 2 statements:
1. This is not an academic exercise, but a real life engineering problem which I'm not at leisure to disclose all the finer details of.
2. This problem will get more complicated as the discussion evolves.
Background:
1. There are two hydraulic cylinders with sheaves mounted on either end, and the cylinder/sheave assemblies are mounted on trollies which can be moved in and out, either in unison or independently. For the beginning of the discussion we will assume they move in unison.
2. There is a wire wrapped around the 4 sheaves
3. There is a load cell between one of the sheaves and one of the cylinders
4. There are two possible modes of operation of the cylinders: 1. they can be controlled by a hydraulic pressure regulator, or 2. by a load holding hydraulic circuit that once desired tension is reached, closes and locks tension value in. For the beginning of the discussion we will assume that the cylinders are controlled by regulator.
5. I need to calculate 1. Tension in the wire and 2. force applied to an object by the wire, as the trollies move forward and press the wire against the object. For the beginning of the discussion, we will assume that I've already got #1 figured out and we are only concerned with #2.
Here is a basic diagram, before the trollies move forward:
The trollies can move (in unison) up toward the top of your page and down toward the bottom. They cannot move side-to-side to any appreciable degree other than that which is caused by minimal flexing of the structure they are mounted on (not shown).
So, we assume that the cylinders are controlled by a hydraulic pressure regulator. We set the regulator to 100PSI and for example this results in 100lbs of tension in the wire. If we were to grab the wire from any side and drag it in toward the center, the cylinders would give way as the fluid inside is compressed >100PSI and is relieved by the pressure regulator. So if you were strong enough, you could pull the wire all the way until the cylinders bottom out, and then you would not be able to pull any further.
Here is a basic diagram of the cylinders moving in (driving up toward the top of your page in unison) and pressing the wire against an object:
Note that the cylinders have compressed a little bit, and there is now a 30 degree angle of deflection on both sides of the object. While the cylinders did compress, the travel of the cylinders was not as great as the travel of the trollies.
Now, if there were no preexisting tension in the wire, the tension in the wire should be exactly equal to the force applied to the object by the wire, because of the 30 degree angles. The two forces will/should be equal at (and ONLY at) this specific angle of 30 degrees, as demonstrated by this load rigging diagram:
BUT we cannot assume that the same holds true if there is preexisting tension in the wire (as in, hydraulic cylinders are pressurized by the regulator to 100PSI/100LBS tension before moving in).
Here is the formula that I'm currently using to calculate the force applied by the wire:
I have tested this formula with an array of load cells and proven it accurate in calculating the force given the tension and the deflection angles, but only when preexisting tension is zero. I do not currently have the hydraulic pressure regulator described above. I only have the hydraulic locking circuit, so the cylinders cannot give way. Without the regulator, I can only achieve about 10 degrees of deflection, and this is only possible by the structure flexing and the wire stretching. If I use any preexisting tension with this setup, my formula is wildly inaccurate.
I am looking to upgrade to the pressure regulator setup, and my first question is: If I install the regulator so that tension remains constant as the cylinder compress, will this formula [specifically the part (Tension_Lbs-Preexisting_Tension)] accurately describe the force applied to the object?
1. This is not an academic exercise, but a real life engineering problem which I'm not at leisure to disclose all the finer details of.
2. This problem will get more complicated as the discussion evolves.
Background:
1. There are two hydraulic cylinders with sheaves mounted on either end, and the cylinder/sheave assemblies are mounted on trollies which can be moved in and out, either in unison or independently. For the beginning of the discussion we will assume they move in unison.
2. There is a wire wrapped around the 4 sheaves
3. There is a load cell between one of the sheaves and one of the cylinders
4. There are two possible modes of operation of the cylinders: 1. they can be controlled by a hydraulic pressure regulator, or 2. by a load holding hydraulic circuit that once desired tension is reached, closes and locks tension value in. For the beginning of the discussion we will assume that the cylinders are controlled by regulator.
5. I need to calculate 1. Tension in the wire and 2. force applied to an object by the wire, as the trollies move forward and press the wire against the object. For the beginning of the discussion, we will assume that I've already got #1 figured out and we are only concerned with #2.
Here is a basic diagram, before the trollies move forward:
The trollies can move (in unison) up toward the top of your page and down toward the bottom. They cannot move side-to-side to any appreciable degree other than that which is caused by minimal flexing of the structure they are mounted on (not shown).
So, we assume that the cylinders are controlled by a hydraulic pressure regulator. We set the regulator to 100PSI and for example this results in 100lbs of tension in the wire. If we were to grab the wire from any side and drag it in toward the center, the cylinders would give way as the fluid inside is compressed >100PSI and is relieved by the pressure regulator. So if you were strong enough, you could pull the wire all the way until the cylinders bottom out, and then you would not be able to pull any further.
Here is a basic diagram of the cylinders moving in (driving up toward the top of your page in unison) and pressing the wire against an object:
Note that the cylinders have compressed a little bit, and there is now a 30 degree angle of deflection on both sides of the object. While the cylinders did compress, the travel of the cylinders was not as great as the travel of the trollies.
Now, if there were no preexisting tension in the wire, the tension in the wire should be exactly equal to the force applied to the object by the wire, because of the 30 degree angles. The two forces will/should be equal at (and ONLY at) this specific angle of 30 degrees, as demonstrated by this load rigging diagram:
BUT we cannot assume that the same holds true if there is preexisting tension in the wire (as in, hydraulic cylinders are pressurized by the regulator to 100PSI/100LBS tension before moving in).
Here is the formula that I'm currently using to calculate the force applied by the wire:
Code:
Force_Applied_to_Object:= (Tension_Lbs-Preexisting_Tension)*(SIN(Left_Deflection_Angle)+SIN(Right_Deflection_Angle));
I am looking to upgrade to the pressure regulator setup, and my first question is: If I install the regulator so that tension remains constant as the cylinder compress, will this formula [specifically the part (Tension_Lbs-Preexisting_Tension)] accurately describe the force applied to the object?