Ma th em a t ic a l Analysis (4 points) A double-acting hydraulic cylinder is us

Question

Mathematical Analysis (4 points)

A double-acting hydraulic cylinder is used to actuate a linear joint of an industrial robot. The inside diameter of the cylinder is 3.5 in. The piston rod has a diameter of 0.5 in. The hydraulic power source can generate up to 500 lb/in2 of pressure at a flow rate of 1200 in3/min to drive the piston.

Determine the following:

i.      The maximum velocity of the piston and the maximum force that can be applied in the forward stroke.

ii.      The maximum velocity of the piston and the maximum force that can be applied in the reverse stroke.

Hints:

Velocity:           V = Q/A

§    V = Velocity of Piston

§    A = Area of cylinder cross section,

§    Q = volumetric flow rate,

Applied Force, F = p A

§    F = Applied force

§    p = fluid pressure

§    A = Area of cylinder cross section, m2 (in2)

Explanation / Answer

Ans.Forward stroke area=0.25 *3.14*(3.5)2=9.62 in2

Reverse stroke area=0.25*3.14*(0.5)2=9.42 in2

A.Forward stroke velocity V=1200/9.62=124 in/min

F=500*9.62=4810 b

B.Reverse stroke velocity V=1200/9.42=127.4 in/min

F=500*9.42=4710 b

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