UBC Theses and Dissertations

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UBC Theses and Dissertations

Position-dependent dynamics and stability of machine tools Law, Mohit


Machine tool’s productivity and ability to produce a component of the required quality is directly influenced by its dynamic stiffness at the tool center point. Lack of dynamic stiffness may lead to unstable regenerative chatter vibrations which are detrimental to the performance. The chatter vibrations are influenced by the changing structural dynamics of the machine as the tool moves along the tool path, resulting in position-varying machining stability of the system. Evaluation of these varying dynamics at the design stage is a complex process, often involving the use of large order finite element (FE) models. Complexity and computational costs associated with such FE models limit the analyses to one or two design concepts and at only a few discrete positions. To facilitate rapid exploration of several design alternatives and to evaluate and optimize each of their position-dependent dynamic behavior, a generalized bottom-up reduced model substructural synthesis approach is proposed in this thesis. An improved variant of the component mode synthesis method is developed and demonstrated to represent higher order dynamics of each of the machine tool components while reducing the computational cost. Reduced substructures with position-invariant response are synthesized at their contacting interfaces using novel adaptations of constraint formulations to yield position-dependent response. The generalized formulation is used to evaluate the position-dependent behavior of two separate machine tools: one with a serial kinematic configuration, and another with hybrid serial-parallel kinematics. The reduced machine model is verified against full order models and is also validated against measurements by including joint characteristics in the model. The effects of position and feed-direction-dependent compliances on machining stability are investigated by using a novel position and feed-direction-dependent-process-stability performance criterion that evaluates the productivity of machine tools in its entire work volume. Parameters limiting the target productivity levels are identified and modified; and, the complete dynamics are rapidly re-analyzed using the developed models. Optimal design modifications are shown to increase productivity by ~35%. The proposed methods in this thesis enable efficient simulation of structural dynamics, stability assessment as well as interactions of the CNC and cutting process with the machine tool structure in a virtual environment.

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Attribution 2.5 Canada