Design for dynamic stiffness


The response of a structure to a time-varying input depends on mass, stiffness, and damping. High stiffness and damping are each necessary, but not individually sufficient requirements for a precision machine. For analysing performance, differential equations of motion can be derived from Newton’s Law and Hooke’s Law, which, in turn, can be rewritten via Laplace transformations into frequency response functions (FRFs) as steady state solution, e.g. from input force to output displacement. These transfer functions can be expressed in nodal coordinates based on physical properties mentioned above, or alternatively, be rewritten in terms of two modal parameters, viz. eigenfrequency and relative damping, with mass as scaling parameter.

Although the importance of thorough understanding of the relevant dynamics in the design has not changed since the analyses of cam shaft mechanisms, focus has shifted from creating favorable time responses to shaping of FRFs. Driven by developments in optical storage, such as CD and DVD players, and later on semiconductor equipment in the 1990s, the understanding of superposition of mode shapes and optimal actuator and sensor placement to ‘shape’ the dynamic FRFs was key to robust controller design in combination with good performance.


Design principles