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A hydropneumatic elevator consists of a piston-cylinder assembly to lift the elevator cab. Hydraulic oil, stored in an accumulator tank pressurized by air, is valved to the piston as needed to lift the elevator. When the elevator descends, oil is returned to the accumulator. Design the least expensive accumulator that can satisfy the system requirements. Assume the lift is 3 floors, the maximum load is 10 passengers, and the maximum system pressure is \(800 \mathrm{kPa}\) (gage). For column bending strength, the piston diameter must be at least \(150 \mathrm{mm}\). The elevator cab and piston have a combined mass of \(3000 \mathrm{kg}\), and are to be purchased. Perform the analysis needed to define, as a function of system operating pressure, the piston diameter, the accumulator volume and diameter, and the wall thickness. Discuss safety features that your company should specify for the complete elevator system. Would it be preferable to use a completely pneumatic design or a completely hydraulic design? Why?

Step by step solution

01

Determine the Required Force

First, determine the force required to lift the maximum load using the equation \(F = mg\), where \(m\) is the mass i.e. \(3000 \mathrm{kg}\) and \(g\) is the gravitational acceleration, \(9.81 \mathrm{m/s^2}\).

02

Determine the Minimum Piston Pressure

Then, find the minimum pressure that the piston needs to exert in the hydraulic oil such that the cab can be elevated. This can be found by dividing the force by the minimum area of the piston (which can be calculated from the given diameter using the formula \(A = \pi (d/2)^2\)).

03

Determine the Volume of the Accumulator

This can be found using Pascal's Principle, which states that a change in pressure at any point in an enclosed fluid at rest is transmitted undiminished to all points in the fluid. Thus, the volume of the hydraulic fluid displaced when the elevator rises is V = Ah, where \(A\) is the Area of the piston and \(h\) is height of lift (calculated for the 3 floors). This volume V is equal to the volume of accumulator.

04

Determine the Diameter of the Accumulator

Calculate the diameter of the accumulator from the determined volume using the formula for the volume of a cylinder \(V = \pi (d/2)^2 h\). Assume a reasonable height for the accumulator.

05

Calculate Wall Thickness for Safety

The thickness of the walls of the accumulator can be calculated by Safety stress formula \(T = PR/2S\), where \(T\) is wall thickness, \(P\) is pressure, \(R\) is radius of the accumulator tank and \(S\) is the safety stress value which depends on the material used. Choose a typical value of safety stress for steel.

06

Discuss Safety Features & Design Preference

Safety features could include pressure relief valves to prevent pressure build up in the system, safety brakes for freefall protection, interlocks to prevent accidental operation, etc. Whether a pneumatic or hydraulic design is better depends on various factors. Pneumatic systems are simpler and cheaper to install, but hydraulic systems offer smoother and quieter operation, superior speed control, and more power.

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