The poppet of the pressure relief valve must move 0.2 in from the fully closed p

Question

The poppet of the pressure relief valve must move 0.2 in from the fully closed position in order to pass the full pump flow at the PRV setting (full pump flow pressure). The poppet has a 0.85 in3 area on which system pressure acts. Assuming that the relief valve cracking pressure should be 15% higher than the pressure required to overcome the hydraulic cylinder punching operation, find the required a) spring constant of the compression spring in the PRV, b) initial compression of the spring from its free-length condition as set by the spring-adjustment mechanism of the PRV (poppet held against its seat by spring

Explanation / Answer

(a) At full pump flow pressure, the spring force equals to the hydraulic force which acting on the poppet.

Spring Force = Hydraulic Force

k S = PPRV Apoppet

k S = (1698 lb/in2) (0.85 in2)

k S = 1443.3 lb

Where, k = spring constant (lb/in)

S = total spring compression (in)

Then, we have

k [L + (0.2 in)] = (1443.3 lb)

k L + (0.2 in) k = (1443.3 lb)                                                  { eq.1 }

At the cracking pressure of relief valve, the spring force equals to the hydraulic force which acting on the poppet.

Then, we have

k L = Pcracking Apoppet

k L = [(1.10) (1132 lb/in2)] (0.85 in2)

k L = 1058.4 lb                                                             { eq.2 }

Inserting the value of 'kL' in eq.1 & we get

k L + (0.2 in) k = (1443.3 lb)     

(1058.4 lb) + (0.2 in) k = (1443.3 lb)     

(0.2 in) k = [(1443.3 lb) - (1058.4 lb)]

k = [(384.9 lb) / (0.2 in)]

k = 1924.5 lb/in

(b) An initial compression of the spring from its free-length condition which will be given as -

Using eq.2, we have

k L = (1058.4 lb)     

L = [(1058.4 lb) / (1924.5 lb/in)]

L = 0.549 in

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