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Experiment 2-2 Pressure versus Force

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**Experiment 2-2 Objectives:**

1. Describe the relationship between pressure and force. 2. State Pascal’s Law and explain its application in fluid power. 3. Measure the force output of hydraulic cylinders using a load spring. 4. Calculate the theoretical force output of a fluid power cylinder in both extension and retraction.

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Pressure Versus Force In the above illustration, the load applies a downward force as gravity pushes on it. The fluid inside the bottle, a liquid, resists this movement by virtue of its incompressible nature and pressure develops in direct proportion to the force applied.

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**Hydraulic Actuator Force Output Double Acting Cylinder**

Rod End Cap End Double Acting Cylinder Rod Piston Examine the picture above to become familiar with cylinder nomenclature.

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**Hydraulic Actuator Force Output Basic Cylinder Operation**

Fluid moves from the pump or compressor outlet into the cylinder by one of two or more ports. When the incoming fluid makes contact with the piston, movement is created by the fluid displacing the piston against the rod and, subsequently, moving whatever load is in contact with the rod. It follows that some relationship must therefore exist between how much a cylinder can push based on how pressure is supplied to it.

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**Force, Pressure, and Area Relationship**

Blaise Pascal was a 16th century mathematician, physicist, and philosopher. He discovered the above relationship by observing the effect that a trapped fluid had when a force was applied to it. The result, a pressure buildup, is transmitted equally and at right angles to all containing surfaces. What this means is that the behavior of fluids is predictable. In the above illustration, known as the force triangle, the amount of force is determined by multiplying P times A. If one of the bottom elements is to be determined then you would divide F by either P or A. This configuration is the same as Ohm’s Law.

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**F = P x A Calculating Force**

Calculating force is accomplished by multiplying the pressure value times the area value. Pressure is basically the force exerted by the fluid against a moveable object, in most cases discussed, a piston. Area is a two dimensional unit of measure, such as length times width, and represents the total surface area on which pressurized fluid acts. It is the combination of the pressurized fluid acting on a moveable surface that results in force output. Because the values of pressure and area are easily calculated, force is easily calculated and very predictable. In operation, fluid is forced into the cylinder by the pump where, upon contact with the piston, it encounters resistance and pressure

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Calculating Force Cap End Rod End When calculating force on a “differential” style cylinder as shown above, force must be calculated from two directions; extension and retraction. Because of the greater surface area, the cylinder will produce more force from the “cap end” than it will from the “rod” end. When calculating the area of the rod end, first find the area of the piston and then, the area of the rod. Subtract the rod area from the cap end area and you will calculate the annular area.

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Load Spring CAUTION!!! This experiment uses a compression spring that has a return force of several hundred pounds. It is critical that instructions be followed exactly during setup to prevent personal injury and machine damage.

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Load Spring Examine the illustration above to see how the long rod is inserted through the spring to cage it. The rod should have a threaded piece which goes into the cam on the cylinder rod. When properly inserted, there should be no visible thread between the cam and the rod where the two attach. The main reason we are using this spring is because it has a measured “rating” that can, in turn, be used to measure force.

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**Fls = (L – L1) X K Spring Force Formula**

The formula above is based on a spring rate of 294 pounds per inch. What this means is that for every inch you compress this spring, it will push back with a force equivalent to the total amount of compression. For example, lets say you have compressed the spring 2 inches, how much return force would you have? If you multiply 294 times 2, the linear compression in inches, you get 588 pounds of force. It should be obvious that the spring represents a serious hazard if not properly contained.

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**Theoretical and Actual Force**

Theoretical force is the amount of force one would calculate by simply using given values and applying Pascal’s Law. Actual force is what one would calculate based on the length of the load spring. It is meant for the two to be compared and examined. As you read the instructions please note that you will start with the large bore cylinder, proceeding to the small bore cylinder. The only way to compress the spring using the small bore cylinder is to insert the spring behind the cam. This should become obvious to you as you read the instructions.

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**Review 1. Describe the relationship between pressure and force.**

2. State Pascal’s Law. 3. Calculate the force output on extension of a cylinder given the following information. Given: Piston Diameter = 5 cm Rod Diameter = 2 cm Stroke Length = 28 cm Pressure at Cap End = 6980 kPa 4. Calculate the force output of the cylinder in question 3 if the same pressure is applied to its rod end.

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Review 5. If the diameter of a cylinder’s piston increases, does the force output increase, decrease, or stay the same? 6. If the pressure on a cylinder’s piston decreases, does the force output increase, decrease, or stay the same? 7. If the length of cylinder’s stroke increases, does the force output increase, decrease, or stay the same? 8. If the diameter of a cylinder’s rod decreases, does the cylinders force output in retraction increase, decrease, or stay the same. 9. If the diameter of a cylinder’s rod decreases, does the cylinder’s force output in retraction increase, decrease, or stay the same? 10. If a certain cylinder generates 2000 pounds of force at a pressure of 250 psi, how much force would be generated if the pressure were increased to 750 psi?

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Review 11. If a cylinder with a 2 inch diameter piston requires 800 psi in order to move a load, how much pressure would be needed if the cylinder’s piston size were reduced to 1 ½ inches? 12. Why do actual and theoretical values differ? 13. Why does the small bore cylinder produce less force than the large one? 14. What would be the result of increasing pressure on the small bore cylinder. 15. How much return force would the load spring produce if it were compressed by 3 inches?

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