Piezo Stack Under Spring Force Load

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 k_stack and k_load. The free travel X₀ is reduced by a factor dominated by the ratio of the stiffness of stack k_a and load k_load.

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.

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.