Minimization of the residual vibrations of ultra-precision manufacturing machines via optimal placement of vibration isolators

Abstract Ultra-precision manufacturing (UPM) machines are used to fabricate and measure complex parts having micrometer-level features and nanometer-level tolerances/surface finishes. Consequently, low-frequency residual vibrations that occur during the motion of the machines’ axes must be mitigated. A long-standing rule of thumb in vibration isolation system design is to locate the isolators in such a way that all vibration modes are decoupled. This paper uses the 2D dynamics of a passively isolated system to show that coupling the vibration modes of the isolated system by altering the location of the isolators provides conditions which allow for the drastic reduction of residual vibrations. An objective function which minimizes residual vibration energy is defined. Perturbation analyses of the objective function reveal that the recommended practice of decoupling the vibration modes more often than not leads to sub-optimal results in terms of residual vibration reduction. The analyses also provide guidelines for correctly locating the isolators so as to reduce residual vibrations. Simulations and experiments conducted on a passively isolated ultra-precision machine tool are used to validate the findings of the paper; a 5-fold reduction of the dominant residual vibrations of the machine tool is achieved without sacrificing vibration isolation quality (i.e., transmissibility).