Papers by Keyword: Cubic Spline

Abstract: The traditional fixed pitch error compensation method exists some defects, such as sampling points are not comprehensive and the necessary compensation points are easy to miss. Faced with these problems, this paper presented a new pitch error compensation method based on the open numerical control system. With this method, the traditional measurement points were serried, and more pitch error data were measured. Then calculated the error data with the cubic spline interpolation computation method, and the compensation location and value were obtained according to the accuracy requirement. The pitch error compensation was completed when the data inputted into the open numerical control system with a defined format.

Abstract: Cubic motion is a curve that is generated by the integration of Cubic Spline and dynamic of motion. Cubic spline will draw the curve, whilst the dynamic of motion will position the vertices. This embedded motion attribute to the curve will have an advantage to study related to motion of vehicle. The objective of the paper is to demonstrate the advantage of motion attribute in the curve. It is demonstrated by two case studies. The case studies are simulation of traffic flow system and study of vehicle dynamic response.

Abstract: By Changing the key points on the spiral curve, general groove geometry was determined. Considering the simplicity of modeling and analysis, cubic spline function was used to express the general groove profile. By using the boundary fitted coordinate system transformation, irregular computational domain was transferred to regular region; Based on flow conservation principle, finite volume method was applied to discrete compressible Reynolds equation; By the application of Newton-Raphson iteration method for solving algebraic equation, numerical model of general groove dry gas seals was established. When compared sample results with shallow groove theory, the capacity and stiffness of numerical results match well with theoretical ones, verifying the accuracy of novel numerical model. Through analysis of three typical groove seals, spiral groove seal has strongest carrying capacity. Pressure distribution of three groove seals subjects to the law of hydrodynamic pressure effect. And the numerical model established in this paper will offer a general calculate platform for optimization of groove geometry in the future.

Abstract: In order to avoid the problems of existing methods, a numerical simulation method for two-dimensional airflow over complex terrains is developed in this paper for the engineering use of flight dynamics. Based on the potential flow theories, the effects of terrains on the wind field are considered by a serial of two-dimensional vortexes, whose strengths are solved by combining with the ground boundary conditions. Numerical examples are studied by the proposed method, and the method is also evaluated by comparing the results with ones from the existing method. The result shows that the two-dimensional profile of complex terrains could be described by a cubic spline curve precisely. The computation procedure proposed in this paper is very simple and efficient, and it could provide a result of wind field with considerable accuracy. Therefore, this method could be used for flight principle evaluation and flight simulators. Finally, through simulate flight path, discussing effect of terrains on track.

Abstract: Displacement is a very important parameter in the civil engineering safety evaluation. But traditional displacement measurement methods are impractical and inconvenient in application, for the reason of money cost, time invested or labour involve. Spline-method is proposed to describe the displacement curve based on the angle values measured by inclinometers. Cubic spline is chosen for figuring out the inclination function and displacement values all over the structural. Numerical experiments have proved that Spline-method is feasible and has very high precision.

Abstract: The Strength Pareto Evolutionary Algorithm (SPEA) is adopted to find time-jerk synthetic optimal trajectory of a hexapod robot in the joint space. In order to get the optimal trajectory, cubic splines are employed and derived under the constraint condition of via points to assure overall continuity of velocity and acceleration. Taken both the execution time and minimax approach of jerk as objectives, and expressed the kinematics constraints as upper bounds on the absolute values of velocity and acceleration, the mathematic model of time-jerk synthetic optimal trajectory planning is built. Finally, SPEA is adopted to optimize the stair-climbing trajectory of a hexapod robot, the simulation results show that this method can solve the trajectory planning problem effectively, and the stair-climbing trajectory can meet the contradictory objective functions of high speed and low robot vibration well.