Linear time-invariant milling models applicable to chatter suppression system design

  • Authors:

  • Greg Mason;Martin Berg

  • Affiliations:

  • Mechanical Engineering, Seattle University, Broadway and Madison, Seattle WA;Mechanical Engineering, University of Washington, Box 352600, Seattle WA

  • Venue:
  • Systems Analysis Modelling Simulation
  • Year:
  • 2003

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Abstract

Milling models, applicable to chatter suppression system design, are derived by transforming an established nonlinear milling model into linear constant coefficient discrete time models. The derivation initially utilizes either a modified Tustin or zero-order-hold approximation to create a discrete time approximation of the original model. The resulting periodically time varying system, which includes time delays, is then transformed into a system with constants coefficient and no time delays by adding delay states to the system and computing the system's monodromy matrix. The resulting linear models are then compared to the established nonlinear model. The linear models, while of high order, can be used directly to design chatter suppression systems with traditional linear control system design techniques. An example chatter control system is designed using an optimal regulator. The example controller reduces chatter in a milling system with a four tooth cutter in an up-milling configuration.