Natural frequency of a hydraulic cylinder

As a synchronizing cylinder(Figure K 5) with oil spring stiffness.

The oil spring stiffness for cylinder side A and cylinder side B are arranged in parallel and add up to the total oil spring stiffness c ÖL. The volumes in the displacement chambers are as follows: V A = V AL + A · x and

V B = V BL + A (h max — x)

where V AL, V BL = oil volume in the pipes between valve and cylinder.

Assuming the piston is positioned in the centre and the volumes in the connecting lines are the same, where V o = oil volume at each cylinder side, this would give:

The following applies to the differential cylinder (Figure K 6):

For both cylinders, the natural angular frequency is calculated in each case from

With a hydraulic motor [hydrostatic motor] (Figure K 7), the weight m is replaced by the mass moment of inertia I . This gives

where V 2 = displacement for the motor

V o = dead volume for one side

Figure K 5: Natural frequency behaviour for a synchronizing cylinder

Figure K 6: Natural frequency behaviour for a differential cylinder

Figure K 6: Natural frequency behaviour for a differential cylinder