Because of fast frequency response, high stiffness, and displacement resolution, the piezoelectric actuators (PEAs) are widely used in micro/nano driving field. However, the hysteresis nonlinearity behavior of the PEAs affects seriously the further improvement of manufacturing accuracy. In this paper, we focus on the modeling of asymmetric hysteresis behavior and compensation of PEAs. First, a polynomial-modified Prandtl–Ishlinskii (PMPI) model is proposed for the asymmetric hysteresis behavior. Compared with classical Prandtl–Ishlinskii (PI) model, the PMPI model can be used to describe both symmetric and asymmetric hysteresis. Then, the congruency property of PMPI model is analyzed and verified. Next, based on the PMPI model, the inverse model (I-M) compensator is designed for hysteresis compensation. The stability of the I-M compensator is analyzed. Finally, the simulation and experiment are carried out to verify the accuracy of the PMPI model and the I-M compensator. The results implied that the PMPI model can effectively describe the asymmetric hysteresis, and the I-M compensator can well suppress the hysteresis characteristics of PEAs.

Cylindrical shells are principal structural elements that are used for many purposes, such as offshore, sub-marine, and airborne structures. The nonlinear mechanics model of internal blast loading was established to predict the dynamic blast pressure of cylindrical shells. However, due to the complexity of the nonlinear mechanical model, the solution process is time-consuming. In this study, the nonlinear mechanics model of internal blast loading is linearized, and the dynamic blast pressure of cylindrical shells is solved. First, a mechanical model of cylindrical shells subjected to internal blast loading is proposed. To simplify the calculation, the internal blast loading is reduced to linearly uniform variations. Second, according to the stress function method, the dynamic blast pressure equation of cylindrical shells subjected to blast loading is derived. Third, the calculated results are compared with those of the finite element method (FEM) under different durations of dynamic pressure pulse. Finally, to reduce the errors, the dynamic blast pressure equation is further optimized. The results demonstrate that the optimized equation is in good agreement with the FEM, and is feasible to linearize the internal blast loading of cylindrical shells.

Due to the errors of the servo system and the errors of the ball screw drive system, the positioning errors inevitably occur in the process of CNC machine tools. The measurement of traditional equipment is limited by a fixed measurement radius and a single degree of freedom, which can only be measured within a fixed plane. In this paper, four different positioning errors of CNC machine tools are first measured at full scale by using J-DBB (a modified double ball bar with one spherical joint connecting two bars) method. The J-DBB device uses a three-degree-of-freedom spherical joint as a connecting part, which realizes that the measurement radius can be continuously changed, and the measurement space is a spatial sphere. First, the principle of the J-DBB method is briefly introduced. Next, four typical positioning errors of CNC machine tools are analyzed and examined, which contain the uniform contraction error of ball screw and linear grating, periodic error of the ball screw and linear grating, interference of measurement devices error, and opposite clearance error. In the end, the trajectories of the CNC machine tool spindle with a single positioning error are simulated by using the J-DBB method. The results reveal that this method can be used for the positioning error of machine tools, which helps to better understand the spatial distribution of CNC machine tool errors and provides guidance for the reasonable selection of working areas to improve the machining accuracy of parts.