Elastodynamic Optimization of a 5-DoF Parallel Kinematic Machine Considering Parameter Uncertainty

Geometric errors, vibration, and elastic deformation are the main causes for inaccuracy of parallel kinematic machines (PKMs). Instead of tackling these inaccuracies after the prototype has been built, this paper proposes a design optimization method to minimize vibration and deformation considering the effects of geometric errors before constructing the PKM. In this paper, geometric errors are described as parameter uncertainty because they are unknown in design stage. A five degree-of-freedom (DoF) PKM is taken to exemplify this method. Elastodynamic model is first formulated by a step-by-step strategy. On this basis, dynamic performances, including natural frequency, elastic deformation, and maximum stress, are analyzed. These analytical results are verified by finite-element simulation and experiment. Then, the necessity of concerning parameter uncertainty in optimization is addressed. Next, parameter uncertainty is added to the formulation of objectives and constraints by Monte Carlo simulation and response surface method. Finally, elastodynamic optimization of the 5-DoF PKM is implemented to rebuild a prototype which is robust to geometric errors and has minimal vibration and deformation. The proposed method can also be applied to accuracy improvement of any machines in practical applications.