The spring effect of the compressed oil column is decisive for the stiffness of actuators. The dimensions of the actuator also play a role.
In the case of a hydraulic motor with a high response proportional valve, the stiffness ("torsional stiffness") is a function of the displacement volume V 2 and the enclosed volume of liquid V 0 on one side:
![6db24f7fa269d7245afbb735a91ec804e4983243 steifigkeitvonstellantrieben_01.gif](/fileadmin/smc/files/6db24f7fa269d7245afbb735a91ec804e4983243.gif)
with E ‘ = compression module.
The symmetrical conditions and small volume of enclosed liquid (if the valve is fitted directly on the motor), give the hydraulic motor more stiffness than the cylinder, but the leakage losses are also greater.
In the case of the hydraulic cylinder, the stiffness is a function of the piston and rod surface area, the stroke and the volume of liquid enclosed in the pipelines.
In the case of a synchronizing cylinder with a high response proportional valve, the minimum stiffness is located in the middle position of the piston:
![65736eb652266cdba2fbff211a63460588b20c3a steifigkeitvonstellantrieben_02](/fileadmin/smc/files/65736eb652266cdba2fbff211a63460588b20c3a.gif)
with V = volume under pressure, A R = annular area in the cylinder. In the case of the differential cylinder there is an additional factor – the influence of the ratio of the piston surface area to the annular area:
![fade70def7f75cb9fceb9bf837f59907b55099f9 steifigkeitvonstellantrieben_03](/fileadmin/smc/files/fade70def7f75cb9fceb9bf837f59907b55099f9.gif)
with A K = piston surface area.
Cylinders with a large active area and small stroke can be very stiff. In the case of high pressures and strokes, however, they are softer. Stiffness is therefore also a design issue.