The following data refers to a maintenance test with a hydraulic press: • diameter of plunger is 50mm •diameter of ram is 0.2mm •stroke length of plunger is 70cm •effort on the plunger is 310kn determine the following: 1. force exerted by the ram 2. distance moved by the ram per stroke of the plunger 3. the number of pumping strokes required by the plunger to lift the load to a height of 46m.
Are you sure about that Ram diameter?
Rams are usually (much) larger in diameter than the piston/plunger.
0.2 mm is a very small Ram diameter.
Just what is it going to support?
Using Ram diameter = 0.2 mm makes nonsense of the calculations.
I’ve changed the value from 0.2 mm to 0.2 m (1,000 fold larger)
If the Ram diameter actually is supposed to be 0.2 mm then you should amend the calculations below accordingly.
Given Data
Plunger Ram
F1 = 310 KN F2 = ?
d1 = 50 mm = 0.05 m d2 = 0.2m
A1 = πd1^2/4 A2 = πd2^2/4
s1 = 70 cm = 0.7 m s2 = ?
Fluid pressure is constant. i.e. Fluid pressure on piston head is the same as fluid pressure on Ram head.
P = F1/A1 = F2/A2
Work done by the piston is equal to the work done by the Ram. i.e.
WD = F1*s1 = F2*s2
1/ Force exerted by Ram is F2.
Using F1/A1 = F2/A2. Then
F1/F2 = A1/A2 = (πd1^2/4)/( πd2^2/4)
F1/F2 = (d1^2)/(d2^2)
F1/F2 = (d1/d2)^2
Or, F2 = F1.(d2/d1)^2
Then, F2 = 310*10^3*(0.2/0.05)^2 = 310*10^3*4^2 = 4.96 *10^6
Force exerted by the Ram is F2 = 4.96 MN
2/ Using F1*s1 = F2*s2, then
s2 = (F1/F2)*s1
s2 = (310*10^3/4.96*10^6)*0.7 = 0.04375 m (43.75mm)
Distance moved by Ram per stroke of piston = 43.75 mm
3/ Number of strokes required is N = (0verall) distance moved by Ram divided by Ram movement per stroke.
N = 46 m / 43.75 mm
N = 46/0.04375 = 1051.142
Number of pumping strokes required by the plunger is N = 1,052