Probabilistic robustness analysis on the planar parasitic motions of flexural mechanisms with uncertain manufacturing imperfectness

Abstract

In view of various piezoelectric-actuated flexural mechanisms (FMs) can be widely found in many significant precision fields, such as sensors, instruments and micro-machines, this paper will introduce a new stochastic compliance model to theoretically investigate their planar parasitic motions (PPM) induced by uncertain manufacturing imperfectness, which will be constructed by the matrix-based compliance modeling (MCM) method from the viewpoint of statistics and probability. Firstly, a new dimensionless PPM relative ratio, which is mathematically defined to be the relative ratio of parasitic motions to the primary motions, will be introduced to more effectively characterize the adverse PPMs of designed FMs. Secondly, a novel eligible probability (EP), which means the acceptance possibility that the dimensionless PPM relative ratios of imperfect FMs can totally satisfy their allowable designed values, will be innovatively introduced to investigate the influences of uncertain manufacturing imperfectness on the motion accuracies of different FMs from the viewpoint of probability. Then taking two types of powerful FMs as examples, the influences of their dominant dimension parameters on the PPM relative ratios, eligible probabilities (EPs) and output stiffnesses will be analytically revealed and compared based on the built stochastic PPM models. In addition, a novel type of probability and stiffness contours (PSCs) method will be also proposed to design the FMs that have strong robustness to their manufacturing imperfects. Finally, a series of experimental measurements will be conducted on different double parallelogram compliant mechanisms (DPCM) consist of the right circular and leaf spring flexure hinges to validate the feasibility and effectiveness of the proposed stochastic PPM model and PSC method.