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Hydraulic Jack Laboratory Experiment

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Abstract

This paper describes an experimental laboratory procedure for determining the mechanical advantage and efficiency of a small hydraulic jack. The testing procedure and required calculations demonstrate how the efficiency of a simple machine can be determined, and how multiple mechanical advantages in a simple machine have a multiplying effect, rather than an adding effect. The cost to set up the experiment is relatively low and the testing procedure is straightforward, yet very informative for the students.

Introduction

Hydraulic jacks provide a means of lifting loads that otherwise could not be lifted by conventional mechanical (screw and scissors) jacks. A common hydraulic jack with a lever arm and pump has two Mechanical Advantages (MA) built into it. One MA is due to the lever arm and the other is due to the ratio of the ram piston diameter squared (D2) to the pump piston diameter squared (d2), D2 / d2. The two MA’s combine in a manner that results in a multiplying effect rather than an adding effect, which yields a much larger overall MA. The efficiency of a jack can be determined from the basic definition of efficiency, which is output / input. This laboratory exercise is appropriate for mechanical engineering technology or mechanical engineering students for a course in applied fluid mechanics, fluid power or machine design. The needed equipment is readily available off-the-shelf, at a very low cost.

Background

A hydraulic jack has a relatively large overall MA due to the lever arm and the ratio of the ram piston diameter squared to the pump piston diameter squared. The MA due to the lever arm can be demonstrated and determined by analyzing the simple lever arm shown in Figure 1. Point A is the lever arm pivot point, Point B is where the lever arm applies an output force (FOLA = force out, lever arm) to the jack’s pump and Point C is where the input force (FILA = force in, lever arm) to the system is applied, usually by hand.

Experimental Procedure

1. Weigh the weight hanger.

2. Weigh the assorted small weights.

3. Determine the mechanical advantage due to the lever arm on the jack by measuring the lengths l1 and l2, and calculating the ratio l2 / l1.

4. Determine the mechanical advantage due to the ratio of the piston diameters squared by measuring the pump piston and ram diameters, and calculating the ratio D2 / d2. The instructor may choose to disassemble the jack and measure the diameters before the experiment actually takes place to save time.

5. Determine the total mechanical advantage of the jack by multiplying the individual MAs together.

6. Place the jack in the testing apparatus.

7. Place the weight hanger on the end of the hydraulic jack’s lever arm.

8. Add weights to the weight hanger until the jack just starts to lift the beam. Record the amount of weight on the weight hanger and the load cell force.

9. Add large weight(s) to the beam.

10. Adjust the position of the lever arm so that it remains horizontal as the hanger weights are applied to simplify the calculations.

11. Repeat steps 8-10 eight to ten times throughout the load range of the jack.

Student’s Laboratory Report

As a minimum the students should include the following in their report of the results.

1. Tabulated jack efficiency data for each weight lifted.

2. A graph of the force applied to the lever arm versus the jack’s output force.

3. A graph of the jack efficiency versus the jack’s output force.

4. An explanation of why the jack efficiency does not remain constant.

5. An explanation of what the system losses are, and how they effect the shape of the efficiency curve.

6. Determine what the internal pressure inside the jack is when the jack is used to lift a load equal to its rated capacity.