The nonlinear dynamics model of gearing system is developed based on RV transmission system. The influence of the nonlinear factors as time-varying meshing stiffness, backlash of the gear pairs and errors is considered. By means of the Lagrange equation the multi-degree-of-freedom differential equations of motion are derived. The differential equations are very hard to solve for which are characterized by positive semi-definition, time-variation and backlash-type nonlinearity. And linear and nonlinear restoring force are coexist in the equations. In order to solve easily, the differential equations are transformed to identical dimensionless nonlinear differential equations in matrix form. The establishment of the nonlinear differential equations laid a foundation for The Solution of differential equations and the analysis of the nonlinearity characteristics.

When there is an obvious large‐scale bias between a regional simulation and its driving global analysis, the regional model will provide inaccurate background information for radar data assimilation, which may eventually yield location errors associated with predicted precipitation. A case study of a squall line over the Yangtze‐Huaihe river basin presents such a situation. In this regard, we propose an approach to incorporate a large‐scale constraint into radar data assimilation to mitigate the effects of large‐scale bias on analysis and forecast results, in which global analysis data are introduced into the regional model using the spectral nudging technique to improve the quality of the first guess and background error statistics in radar data assimilation. A series of experiments are conducted with the Weather Research and Forecasting model and its three‐dimensional variational system to investigate the effectiveness of the proposed approach to introduce a large‐scale constraint into radar data assimilation. The experimental results demonstrate that the introduction of global analysis data can effectively correct the large‐scale bias and significantly improve the forecast skill of large‐scale patterns and convection initiation. The background error covariance (BE) obtained with the large‐scale constraint plays an important role in improving the assimilation effect. The length scales of BE are reduced after the large‐scale bias is removed, which represents a partial solution to the overestimation of BE reported in previous studies. In addition, applying a larger nudging wave number to radar data assimilation domain is not appropriate because the use of a larger wave number can negatively impact the three‐dimensional variational analysis.

No abstract

Abstract：This paper analyses the causes and effective estimation method of nonlinear error; By machine tool motion solution, established a five-axis machine tool BV100 motion transformation mathematical models, combined with linear interpolation principle established the error compensation and nonlinear motion error model of the machine tool .by VB language, developed nonlinear error compensation function of special post process; and through the impeller cutting experiment validate the processor is correct and practical.