Piezo Stack Under Spring Force Load

Piezo stack theory
Piezo Stack - Spring Type Load Case

In case of a spring type load the displacement of the stack will be reduced with regard to the initial free displacement X0. The achievable displacement is determined by the elastic equilibrium of the counteracting compression of the spring and the piezo stack which are represented by the stiffness factors kstack and kload. The free travel X0 is reduced by a factor dominated by the ratio of the stiffness of stack ka and load kload.

The formula suggests, that the actuator stiffness has to be high in comparison with the load to in order to maximize the useable displacement of a piezo stack.

In case of a spring-type load an actuator stack has to chosen which free displacement is larger by a factor than the maximum given displacement X:    

The blocking force of the actuator stack has also to be chosen by the same factor larger than the max load force.

Piezo stack theory
Piezo stack displacement when loaded by a spring type force

The equilibrium can also be determined graphically in a displacement-force diagram. The following figure explains the case of a soft spring load as well as a stiff load, where resulting displacements are smaller. The dotted lines of load crosses the lines (solid) which represent the actuator at different voltages. 

Piezo stack theory
Piezo stack displacement