TCP interpolation with look-ahead function for five-axis machining

A method for direct evaluation of the dynamic 3D path accuracy of NC machine tools

The smoothness of tool trajectories would be as important as that of axis trajectories for five-axis machining. The present study proposes a geodesic interpolation for five-axis machine tools. The tool positions and orientations are fitted to geodesics, respectively, to achieve smooth accurate motions of the tool center point (TCP), smooth axis motions, and the constant velocities of the TCP position and orientation. Not only the linear and circular geodesic interpolation are proposed, but also the acceleration/deceleration and block connection schemes are considered. The method is illustrated by simulations and experiments on a five-axis machining center, and compared to the interpolator with the TCP control. The real-time implementation of geodesic interpolation is well within the scope of modern CNC systems.

Adaptive learning control for thermal error compensation of 5-axis machine tools

Thermal deformation via the temperature change is the most significant factor influencing the machine tools’ precision accuracy. Among the thermal deformation, the spindle deformation has the most severe effect on the tool center point (TCP), followed by deformation of linear movement. Hence, this study proposes a method that combined the chromatic confocal displacement sensor and an artificial neural network to compensate thermal deformation of TCP via coupling the influence of linear axis movement and spindle rotation. The results show that the proposed method can effectively restrain the thermal deformation of TCP within the range of 4um during machining.

In practical machining, flank milling path generation methods of blade surfaces should concern machine axes’ motions to improve machined surface quality, as well as the gouging-avoidance with the hub surface and the geometric deviation constraints. The smoothness of the tool orientation in the part coordinate system cannot assure the smooth rotary axis motions of a five-axis machine tool, since the conversion of tool orientation from the part coordinate system to the machine coordinate system is nonlinear. A flank milling path is represented with the cutter reference point trajectory and the displacement curves of the two rotary axes in this research, so that the machine axes’ motions along the tool path can be directly smoothed when generating the path. The point-to-surface distance function is adopted to evaluate the geometric deviation, and an algorithm based on the differential evolution algorithm is presented to solve the distance function robustly. The sum of the squares of the first, second, and third derivatives of the cutter reference point trajectory and the two rotary axes’ displacement curves are adopted as the smoothness indicators. Then, a flank milling path generation model for blade surface smoothing the machine axes’ motions and considering the hub surface gouging-avoidance and geometric deviations constraints is developed. Numerical examples and machining experiments for five-axis flank milling of a blade surface are given to confirm the validity and effectiveness of the proposed approach.

A new spectral meshless radial point interpolation (SMRPI) method for the two-dimensional Fredholm integral equations on general domains with error analysis

In this article, recently proposed spectral meshless radial point interpolation (SMRPI) method is applied to the two-dimensional diffusion equation with a mixed group of Dirichlet's and Neumann's and non-classical boundary conditions. The present method is based on meshless methods and benefits from spectral collocation ideas. The point interpolation method with the help of radial basis functions is proposed to construct shape functions which have Kronecker delta function property. Evaluation of high-order derivatives is possible by constructing and using operational matrices. The computational cost of the method is modest due to using strong form equation and collocation approach. A comparison study of the efficiency and accuracy of the present method and other meshless methods is given by applying on mentioned diffusion equation. Stability and convergence of this meshless approach are discussed and theoretically proven. Convergence studies in the numerical examples show that SMRPI method possesses excellent rates of convergence.

In this paper, a pseudospectral meshless radial point interpolation (PSMRPI) technique is applied to the three-dimensional wave equation with variable coefficients subject to given appropriate initial and Dirichlet boundary conditions. The present method is a kind of combination of meshless methods and spectral collocation techniques. The point interpolation method along with the radial basis functions is used to construct the shape functions as the basis functions in the frame of the spectral collocation methods. These basis functions will have Kronecker delta function property, as well as unitary possession. In the proposed method, operational matrices of higher order derivatives are constructed and then applied. The merit of this innovative method is that, it does not require any kind of integration locally or globally over sub-domains, as it is essential in meshless methods based on Galerkin weak forms, such as element-free Galerkin and meshless local Petrov–Galerkin methods. Therefore, computational cost of PSMRPI method is low. Further, it is proved that the procedure is stable with respect to the time variable over some conditions on the 3D wave model, and the convergence of the technique is revealed. These latest claims are also shown in the numerical examples, which demonstrate that PSMRPI provides excellent rate of convergence.

Research on generation of toolpaths with smooth tool orientation changes for five-axis machining of blisk based on the rotary axes kinematic features of machine tool

Previous works solve the time-optimal path tracking problems considering piece-wise constant parametrization for the control input, which may lead to the discontinuous control trajectory. In this paper, a practical smooth minimum time trajectory planning approach for robot manipulators is proposed, which considers complete kinematic constraints including velocity, acceleration and jerk limits. The main contribution of this paper is that the control input is represented as the square root of a polynomial function, which reformulates the velocity and acceleration constraints into linear form and transforms the jerk constraints into the difference of convex form so that the time-optimal problem can be solved through sequential convex programming (SCP). The numerical results of a real 7-DoF manipulator show that the proposed approach can obtain very smooth velocity, acceleration and jerk trajectories with high computation efficiency.

The present authors pointed out in the previous paper [1] that the implicit SMAC scheme is quite efficient and non-staggered grid arrangement can decrease the computational effort and save the storage memory which is very important to the direct numerical simulation (DNS) of complicated 3-D flow fields. But using non-staggered grid arrangement, the pressure field oscillation (PFO) ordinarily occurs and also, the pressure on the solid walls including sharp corners need to be prescribed directly as the pressure boundary conditions. In this paper, a new interpolation method, which is a modification to Cheng and Armfield's interpolation formulation, is presented in order to completely prevent PFO from occurring, Moreover, a more accurate specification method of wall pressures and special treatment of pressures at sharp corners are proposed. To test the new methods proposed, the DNS of flow past a square cylinder and flows over backward-facing steps, which are typical of the flow fields with sharp corners, is made using the implicit SMAC scheme combined with these methods. The calculated results are compared with the previous experimental and numerical data and show good agreement with them.

In high-speed precision machining systems, trajectory requires very small feedrate fluctuation and contour error, which can be achieved with pazametric interpolation. This paper proposes aspeed-controlled interpolation method based on optimal-feedrate algorithm. The real-time interpolation method was taken full its advantages, the chord error and the difference between the orientation of tangent vector of the curve at current point and previous point were repeatedly checked through the whole interpolation process. If either chord error exceeded the prescribed tolerance or sharp corner was detected, the feedrate in the proposed interpolation method was automatically adjusted in order to confine the chord error within the prescribed tolerance. A parametric curve, determined by the non-uniform rational B-spline (NiJRBS), was employed to test the feasibility and precision of the proposed interpolation method.

Simultaneous rotary-translational (R-T) axis motion error has significant influence on multi-axis machine tool precision. To improve multi-axis machine tool precision, axis motion error measurement and trace method are investigated in this study. A sensorless R-T axis motion error measurement and trace technology based on virtual bar is proposed. Firstly, the fundamental sensorless test principle is discussed. Then, the virtual-bar-based test path of a circular test though a rotary axis and two translational axes motion is scheduled. The mathematical model of motion error is established. Furthermore, to identify the error source, spatial error charts and some advanced signal processing and feature extraction technologies, such as wavelet transform and frequency analysis, are used. The analysis of experimental results shows that it is practical and efficient to use the virtual bar and the sensorless information to estimate motion error.

This article is devoted to showing the efficiency and accuracy of two numerical procedures for the numerical solution of the capillary formation in tumor angiogenesis. A meshless local radial point interpolation (MLRPI) scheme based on Galerkin weak form is analyzed. The reason for choosing MLRPI approach is that it does not require any background integration cells; instead, integrations are implemented over local quadrature domains, which are further simplified for reducing the complication of computation using regular and simple shape. The spectral meshless radial point interpolation (SMRPI) method does not need any integration. The radial point interpolation method is proposed to construct shape functions for MLRPI and basis functions for SMRPI. A weak formulation with a Heaviside step function transforms the set of governing equations into local integral equations on local subdomains in MLRPI, whereas the operational matrices convert easily the governing equations (even high order) into a linear system of equations in SMRPI. The finite difference technique is employed to approximate the time derivatives. A stability analysis technique based on the eigenvalue of the matrices is employed to check the stability condition for the presented meshless methods. Furthermore, the methods are successfully applied to solve the problem with high values of the cell diffusion constant which many of the available methods did not investigate for solving these cases. Because of non-availability of the exact solution, we consider two strategies for checking the stability of time difference scheme and for surveying the convergence of the fully discrete scheme. From numerical results, it is considerable that the present methods provide the similar results. Moreover, less CPU time and less computational complexity are two advantages of the SMRPI method with respect to the MLRPI method.

Machining centers are the highest-valued and most widely used production tools in Japan. Accuracy inspections of machining centers are performed following ISO standards. One of the basic acceptance tests is to verify the positioning accuracy of the linear axes. The positioning accuracy of a single linear or rotary axis can be easily corrected by a numerical control device if the error is known. The error motion of a single linear axis has six degrees of freedom, including the positioning motion. Recently, a laser interferometer that can measure the 6-DOF error motion simultaneously has been developed. This study proposes a method for measuring the positioning accuracy in three dimensions for daily inspection to quickly identify changes in the positioning accuracy. The effectiveness of the proposed method was investigated by image matching of speckle patterns.