PRINCIPLES OF CALCULATION FOR HYDRAULICS
The calculation examples on the side are essential for the use of hydraulic systems.
Lifting force of a hydraulic cylinder
The lifting force of a hydraulic cylinder is derived from the pressure p ( bar) exerted in the hydraulic cylinder on its piston.
Formula:
F(kg) = p(bar) .
A(cm² )
[for g = [(10 N.m) : s²]]
Where:
F = force acting on the cylinder in kg
p = operating pressure in bar
A = piston area in the cylinder in cm² resulting from the piston diameter:
A (cm²) = [d (mm)². 3.1416] : 400
Example: Identifying operating pressure
A load of 72 t is to be lifted with a cylinder.
What operating pressure is required?
A (cm²) = [d (mm)².3,1416]: 400
with a piston diameter d = 130 mm
A = (130².3,1416) : 400 cm²=132.7 cm²
For F(kg) = p(bar) .
A(cm 2 ) is obtained after conversion
p(bar) = F (kg) : A (cm²) where F = 72 t = 72,000 kg
p = 72,000 : 132.7 bar = 542 bar.
Result: The required operating pressure is 542 bar.
Example: Calculating the weight of the lifted load
A load whose weight is unknown is lifted with a cylinder.
The pressure gauge indicates an operating pressure of 520 bar.
The following formula is used to calculate the weight of the lifted load:
A (cm²) = [d (mm)² . 3.1416] : 400
with a piston diameter -> d = 45 mm
A = (45² . 3.1416) : 400 = 15.9 cm²
F (kg) = p(bar) .
A(cm² )
F = (520 . 15.9) kg = 8270 kg
Result: The lifted load weighs 8270 kg.
By operating a hydraulic cylinder with a hand pump, the cylinder makes a certain stroke at each pump stroke that depends on the area of the piston and the flow rate of the pump at each pump stroke.
For two-stage pumps, the low-pressure flow rate BP and the high-pressure flow rate AP should be set for cylinder movement without load, and for movement under load.
Formula:
S(mm) = [V (cm³).10.]: A (cm²)
Where:
v = cylinder speed in mm/s
Q = pump flow rate in l/min
A = piston area in the cylinder in cm 2
Example: Calculation of load displacement at pumping
A cylinder is operated with a hand pump .
What displacement does the load make with each pumping?
-> A= 15.9 cm²
S(mm) = [V(cm³) .10]: A (cm²)
Pump drive
With a flow rate at each pump stroke
V = 3.5 cm³
S =( 3.5 .10) : 15.9 mm = 2.2 mm
Result: With each pumping, the load shifts 2.2 mm
Example: How many pumps are needed to extend the whole cylinder
A cylinder (stroke H=50 mm) is operated with a hand pump .
A vacuum stroke L = 30 mm must be performed. How many pump strokes are needed to achieve full extension of the cylinder?
-> A = 132.7 cm² (as in example 1)
For the no-load run, the following applies.
S BP (mm) =[V BP (cm³).10]: A (cm²)
With a flow rate at each pump stroke
-> V BP = 32cm³
-> S BP = (32.10) : 132.7 mm = 2.4 mm
Number pumped for no-load stroke: you divide the no-load stroke by the stroke with each pumping:
PB BP = L (mm) : S BP (mm) = 30 : 2.4 = 13 pumps
For running under load:
S AP (mm) =é V AP (cm³).10] : A (cm²)
With a flow rate at each pump stroke
-> V AP = 3 cm³
-> S AP =(3.10) : 132.7 mm = 0.23 mm
Number of pump strokes for running under load: divides the remaining stroke by the stroke completed at each pump stroke:
PB A = [H(mm) – L(mm)] : S AP(mm)= [50-30]: 0.2 =87 pumping
Result: In total = PB BP + PB AP = 13 + 87 = 100 pumps.
Extension speed
The extension speed of a hydraulic cylinder operated with an electric pump depends on the area of the piston in the cylinder and the flow rate of the electric pump.
For two-stage pumps, the low-pressure flow rate Q BP should be set for cylinder movement without load, and the high-pressure flow rate Q AP should be set for movement under load instead.
Formula:
v(mm/s) = [Q(l / min).166,67]: A (cm²)
Where:
v= cylinder speed in mm / s
Q= pump flow rate in l / min
A= area of the piston in the cylinder in cm²
Example: With what speed does a cylinder driven by electric pump extend
A cylinder is operated with an electric pump .
With what speed does the cylinder make its extension?
-> A = 132.7 cm² (as in example 1)
v(mm/s) = [Q(l / min).166,67]: A (cm²)
For pump flow rate -> Q = 1.8 l/min
V= 1,8.166,67 : 132.7 mm/s= 2.2 mm/s
Result: The extension speed of the cylinder is 2.2 mm/s.
