Nonlinear Error Compensation Based on the Optimization of Swing Cutter Trajectory for Five-Axis Machining

In order to solve the problem of deviation between actual and theoretical machining paths due to the presence of rotation axis in five-axis machining, an interpolation algorithm based on the optimization of swing cutter trajectory and the method of corresponding nonlinear error compensation are proposed. Taking A-C dual rotary table five-axis machine tool as an example, the forward and reverse kinematic model of the machine tool is established according to the kinematic chain of the machine tool. Based on the linear interpolation of rotary axis, the generation mechanism of nonlinear error is analyzed, the modeling methods of cutter center point and cutter axis vector trajectory are proposed respectively, and the parameterized model of swing cutter trajectory is formed. The formula for the nonlinear error is obtained from the two-dimensional cutter center point trajectory. According to the established model of swing cutter trajectory, the synchronous optimization method of cutter center point trajectory and cutter axis vector trajectory is proposed, and the nonlinear error compensation mechanism is established. First, pre-interpolation is performed on the given cutter location data to obtain a model of the swing cutter trajectory for each interpolated segment. Then the magnitude of the nonlinear error is calculated based on the parameters of the actual interpolation points during formal interpolation, and the interpolation points with large errors are compensated for the nonlinear error. The simulation results show that the proposed method can effectively reduce the impact of nonlinear errors on machining, and is of high practical value for improving the accuracy of cutter position and the quality of complex free-form machining in five-axis machining.

Application of Adaptive Robust CKF in SINS/GPS Initial Alignment with Large Azimuth Misalignment Angle

When the strapdown inertial navigation system does not perform coarse alignment, the misalignment angle is generally a large angle, and a nonlinear error model and a nonlinear filtering method are required. For large azimuth misalignment, the initial alignment technology with a large azimuth misalignment angle is researched in this paper. The initial alignment technology with a large azimuth misalignment angle is researched in this paper. First, the SINS/GPS nonlinear error model is established. Secondly, in the view of observation gross errors and inaccurate noise statistical characteristics, an adaptive robust CKF algorithm is proposed. Finally, according to the simulation analysis and experiment, the adaptive robust CKF algorithm can augment the stability and improve the filter estimation precision and convergence rate.

Non-binary Nonlinear Error-correcting Codes from Finite Upper Half-planes

Current work builds new families of non-binary nonlinear error-correcting codes from Finite Upper Half-Plane and p a prime number. A fundamental domain is defined to a discrete group acting over Hq. We establish some concepts and results on Hq, such that the geometric properties allow us to get codification and decodification.

Bidirectional Active Piezoelectric Actuator Based on Optimized Bridge-Type Amplifier

Piezoelectric actuators based on bridge displacement amplifying mechanisms are widely used in precision driving and positioning fields. The classical bridge mechanism relies on structural flexibility to realize the return stroke, which leads to the low positioning accuracy of the actuator. In this paper, a series bridge mechanism is proposed to realize a bidirectional active drive; the return stroke is driven by a piezoelectric stack rather than by the flexibility of the structure. By analyzing the parameter sensitivity of the bridge mechanism, the series actuation of the bridge mechanism is optimized and the static and dynamic solutions are carried out by using the finite element method. Compared with the hysteresis loop of the piezoelectric stack, the displacement curve of the proposed actuator is symmetric, and the maximum nonlinear error is improved. The experimental results show that the maximum driving stroke of the actuator is 129.41 μm, and the maximum nonlinear error is 5.48%.

Vibration Error Correction for the FOGs-Based Measurement in a Drilling System Using an Extended Kalman Filter

Fiber-optic gyroscopes (FOGs)-based Measurement While Drilling system (MWD) is a newly developed instrument to survey the borehole trajectory continuously and in real time. However, because of the strong vibration while drilling, the measurement accuracy of FOG-based MWD deteriorates. It is urgent to improve the measurement accuracy while drilling. Therefore, this paper proposes an innovative scheme for the vibration error of the FOG-based MWD. Firstly, the nonlinear error models for the FOGs and ACCs are established. Secondly, a 36-order Extended Kalman Filter (EKF) combined with a calibration method based on 24-position is designed to identify the coefficients in the error model. Moreover, in order to obtain a higher accurate error model, an iterative calibration method has been suggested to suppress calibration residuals. Finally, vibration experiments simulating the drilling vibration in the laboratory is implemented. Compared to the original data, compensated the linear error items, the error of 3D borehole trajectory can only be reduced by a ratio from 10% to 34%. While compensating for the nonlinear error items of the FOG-based MWD, the error of 3D borehole trajectory can be reduced by a ratio from 44.13% to 97.22%. In conclusion, compensation of the nonlinear error of FOG-based MWD could improve the trajectory survey accuracy under vibration.

Five-axis Tri-NURBS Spline Interpolation Method Considering Nonlinear Error Compensation and Correction of CC Paths

In order to improve the accuracy of tool axis vector position and direction in traditional five-axis NURBS interpolation methods and the controlling accuracy of cutter contacting(CC) paths between cutter and work-piece, a five-axis Tri-NURBS spline interpolation method is presented in this article. Firstly, the spline interpolation instruction format is proposed, which includes three spline curves, such as CC point spline, tool center point spline and tool axis point spline. The next interpolation parameter is calculated based on the tool center point spline combined with the conventional parametric interpolation idea. Different from the traditional spline interpolation using the same interpolation parameter for all spline curves, the idea of equal ratio configuration of parameters is proposed in this paper to obtain the next interpolation parameter of each spline curve. The next interpolation tool center point, tool axis point and CC point on the above three spline curves can be obtained by using different interpolation parameters, so as to improve the accuracy of tool axis vector position and direction. Secondly, the producing mechanism of CC paths’ nonlinear error of the traditional spline interpolation is analyzed and the mathematical calculation model of the nonlinear error is established. And then, the nonlinear error compensation and correction method is also put forward to improve the controlling accuracy of CC paths. In this method, the next CC point on the cutter can be firstly obtained according to the next interpolation tool center point, tool axis point and CC point on the three spline curves. And then, the error compensation vector is determined with the two next CC points. To correct the nonlinear error between the next CC point on the cutter and the CC point spline curve, the cutter is translated so that the two next CC points can be coincided. In the end, the new tool center point and tool axis point after translation can be calculated to obtain the motion control coordinates of each axis of machine tool. The MATLAB software is used as simulation of the real machining data. The results show that the proposed method can effectively reduce the CC paths’ nonlinear error. It has high practical value for five-axis machining in effectively controlling the accuracy of CC paths and im-proving the machining accuracy of complex surfaces.