Five-axis trajectory generation considering synchronisation and nonlinear interpolation errors

This paper presents a novel real-time interpolation technique for 5-axis machine tools to attain higher speedand accuracy. To realize computationally efficient real-time interpolation of 6DOF tool motion, a joint workpiece-machine coordinate system interpolation scheme is proposed. Cartesian motion of the tool centre point (TCP) isinterpolated in the workpiece coordinate system (WCS), whereas tool orientation is interpolated in the machinecoordinate system (MCS) based on the finite impulse response (FIR) filtering. Such approach provides several ad-vantages: i) it eliminates the need for complex real-time spherical interpolation techniques, ii) facilitates efficientuse of slower rotary drive kinematics to compensate for the dynamic mismatch between Cartesian and rotary axesand achieve higher tool acceleration, iii) mitigates feed fluctuations while interpolating near kinematic singulari-ties. To take advantage of such benefits and realize accurate joint WCS-MCS interpolation scheme, tool orientationinterpolation errors are analysed. A novel approach is developed to adaptively discretize long linear tool movesand confine interpolation errors within user set tolerances. Synchronization errors between TCP and tool orienta-tion are also characterized, and peak synchronization error level is determined to guide the interpolation parameterselection. Finally, blending errors during non-stop continuous interpolation of linear toolpaths are modelled andconfined. Advantages of the proposed interpolation scheme are demonstrated through simulation studies and vali-dated experimentally. Overall, proposed technique can improve cycle times up to 10% while providing smooth and accurate non-stop real-time interpolation of tool motion in 5-axis machining.

On the use of outgoing longwave radiation data in incorporating divergent part of the wind in analysis

In the present study, kinematic divergence computed using ECMWF grid point data at 850 hPa is enhanced by using the relationship between OLR and divergence. This new enhanced divergence is used to compute the velocity potential and then, the divergence part of the wind is obtained from velocity potetial. To obtain the rotational part of wind, we computed the vorticity from wind data, and subsequently stream function and obtained and the rotational part of the wind from the stream function. The total wind is the combination of divergent part obtained from modified velocity potential (using OLR data) and rotational part from unmodified stream function. This total wind field is used as initial guess for univariate objective analysis by optimum interpolation scheme so that Initial Guess field contained the more realistic divergent part of the wind. Consequently, the analysed field also will contain the divergent part of the wind.

Data assimilation by the variational method with results for the Indian region

ABSTRACT. The variational method for data assimilation as implemented in the operational scheme at ECMWF is briefly presented. The performance of the variational scheme (3D-Var) with respect to tropical cyclones and the Asian summer monsoon is investigated and compared to the Optimum Interpolation scheme. It is found that the analysis of near-surface winds has improved significantly particularly in the vicinity of tropical storms and depressions. The better analyses have led to improvements in the short range forecasts (day 1 to day 3) of such systems. The summer monsoon appears slightly stronger in the 3D-Var analyses, giving enhanced forecast precipitation over the Western Ghats and over large parts of northern India. Only in the latter of these two areas does this verify with observations. The forecasts for India of geopotential, wind and temperature have improved significantly at all forecast ranges, as verified against own analyses. These results are based on 28 cases in two separate 2-week periods.

An Algebraic Hyperbolic Spline Quasi-Interpolation Scheme for Solving Burgers-Fisher Equations

In this work, the results on hyperbolic spline quasi-interpolation are recalled to establish the numerical scheme to obtain approximate solutions of the generalized Burgers-Fisher equation. After introducing the generalized Burgers-Fisher equation and the algebraic hyperbolic spline quasi-interpolation, the numerical scheme is presented. The stability of our scheme is well established and discussed. To verify the accuracy and reliability of the method presented in this work, we select two examples to conduct numerical experiments and compare them with the calculated results in the literature.

A Numerical Investigation of the Performance of Linear Interpolation Schemes Coupled Finite Volume Method in the Analysis of Confined Convection-Diffusion Turbulent Flow Field

Numerical solutions are never exact due to errors emanating from the scheme used in discretizing the governing equations and the flow domain. For convection-diffusion flow, the magnitude of these errors varies depending on the scheme used to interpolate the nodal values of the flow quantities to the interfaces. An interpolation scheme that minimizes these errors would give results that are consistent to experimental results. This paper documents the performance of three linear interpolation schemes; upwind differencing, central differencing scheme and the hybrid scheme in obtaining temperature profiles for a convection-diffusion turbulent flow field. To eliminate the enormous scales inherent in turbulent flow, the field variables present in the governing equations are decomposed into a mean and a fluctuating component and averaged. The closure problem was solved using the turbulence model. The resulting equations are discretized using the robust finite volume discretization technique. The discretized equations are solved using a segregated pressure-based algorithm. The results revealed that the central difference interpolation scheme generate temperature profiles that were consistent with experimental results of Ampofo and Karayiannis, (2003).

A Scheme for Estimating Time-Varying Wind Stress Drag Coefficient in the Ekman Model with Adjoint Assimilation

In this study, the time-varying wind stress drag coefficient in the Ekman model was inverted by the cubic spline interpolation scheme based on the adjoint method. Twin experiments were carried out to investigate the influences of several factors on inversion results, and the conclusions were (1) the inverted distributions with the cubic spline interpolation scheme were in good agreement with the prescribed distributions of the wind stress drag coefficients, and the cubic spline interpolation scheme was superior to direct inversion by the model scheme and Cressman interpolation scheme; (2) the cubic spline interpolation scheme was more advantageous than the Cressman interpolation scheme even if there is moderate noise in the observations. The cubic spline interpolation scheme was further validated in practical experiments where Ekman currents and wind speed derived from mooring data of ocean station Papa were assimilated. The results demonstrated that the variation of the time-varying wind stress drag coefficient with time was similar to that of wind speed with time, and a more accurate inversion result could be obtained by the cubic spline interpolation scheme employing appropriate independent points. Overall, this study provides a potential way for efficient estimation of time-varying wind stress drag coefficient.