Research On The Feedrate Scheduling And Interpolation Method Of The Freeform Machining

As the development of the aerospace, shipbuilding, biomedical, the manufacturing requirements of the die, aviation camera, biology bone and the blades of aviation engine which have many freeform surface increase. How to realize the high precision and high efficiency freeform manufacturing process under the constraints of the machine ability has attracted many scholars to devote to further researches. In traditional freeform manufacturing process, the tool path curve is separated to the discrete short lines and arcs and then the linear and arc interpolation of the CNC is called. But due to the principle errors of the discrete curves methods and the curvature discontinuity in the bending points, the manufacturing efficiency and precision decrease. Contrasted with linearizing the tool path, the parametric interpolation is widely applied for machining the complex sculptured surfaces due to its high precision and efficiency. But there are still many problems that need to be solved in the parametric interpolation.This dissertation supported by the projects named Chinese National Program on Key Basic Research Project(973 Program)(Grant no. 2011CB706702), “Basic Research on the Fabrication of the Optical Freeform Surface-Project 2: Physical Analysis and Accuracy Control Strategy for the Generation of the Optical Freeform Surface” and National High Technology Research and Development Program(863 Program) of China(Grant no. 2012AA041304) “The key research of the blisk intelligent precision manufacturing” mainly focus on the feedrate scheduling and fast parametric interpolation of the freeform surface. The main research contents and results are listed as follows.Using the predictive scheduling method, a high machining efficiency manufacturing process is scheduled under the constraints of the machine axes and machining process. For a given machine tool, the drive dynamic characteristics and motional smoothness impose restrictions on the velocity, acceleration and jerk of the individual axis, which constructe the constraints in the drive system. For different machining process, the machining quality and efficiency are influenced by the trajectory feedrate, acceleration and jerk, which constructe the constraints in the trajectory system. Due to the curve’s curvature and machine motion structure in freeform manufacturing process, the relationship between the kinematical value of the trajectory system and the kinematical value of the driven system is nonlinear. It is difficult to schedule the feedrate under all the constraints both in the driven system and trajectory system. So, an offline predictive feedrate scheduling method for parametric interpolation considering the constraints in trajectory and drive systems is proposed. A feedrate profile which is calculated by offline numerical integration calculation method is obtained and the feedrate profile satisfies the constraints both in the drive system and drive system. In order to decrease the complexity of the feedrate scheduling, the constraints in the drive system are transformed to the trajectory system by a scaling factor, which decreases the dimension of the constraints. The one-dimensional high order time-optimal problem is solved by numerical calculation method according to bang-bang control method. The predictive method is applied to find the switching points of the jerk. Then a time-optimal feedrate profile under all the constraints is obtained. Both simulations and experiments are carried out to prove the effectiveness of the proposed offline predictive feedrate scheduling method.The feedrate profile which is calculated by numerical integration calculation method is fitted by using segment B-spline and the efficiency of the second order Taylor expression interpolation method is improved by the parallel computation method. For the complexity of the feedrate scheduling method, those processes are almost scheduled offline by using numerical integration method. Therefore, a large number of discrete data points are obtained, they are not convenient for the parametric interpolator and those discrete data points need to be fitted by parameter curves. In order to generate a suitable feedrate profile, a segment feedrate profile fitting method by using B-spline is proposed in this paper. Different from the regular curve fitting, the inappropriate fitting method can generate larger acceleration and jerk that seriously affect the machining accuracy and stability although the feedrate satisfies the error requirements. In this paper, the characteristics of feedrate profile and the cubic B-spline are analyzed, and the feedrate original data points are divided in the discontinuity of the jerk. In each segment, the original feedrate datasets are fitted by the third B-spline feedrate curve using the least square method. Those fitted feedrate profiles are combined to generate a unified feedrate B-spline profile. The unified fitted federate profile and the tool path trajectory are used in the controller to command the axis. Due to the real-time calculation requirements of the parametric interpolation, the computation complexity is limited. In order to improve the real-time calculation efficiency, the process of parametric interpolation is separated into the arc-length calculation process and the curve parameter calculation process. By using parallel computation, the two processes are calculated simultaneously in the controller and the computational efficiency is improved. Both simulation and experiment are carried out to verify that the fitted feedrate profile satisfies the error requirements and the novel interpolation can be applied to the controller appropriately.The relationship between the curve’s parameter and arc-length is fitted by NURBS offline, the fitted curve’s parameter and arc-length NURBS is used in real time interpolation. Due to the calculation efficiency, computation precise and robustness are always contradicted in the traditional interpolation methods, a fast NURBS fitting interpolation method is proposed. Firstly, a series of curve parameters and arc-length datasets are obtained by adaptive Gauss numerical integration method and those datasets are fitted by NURBS. In order to improve the fitting precision and decrease the number of the fitting curve’s parameter, the origin curve’s parameter and arc-length datasets are divided according to the third derivative of the curve’s parameter respect to the curve’s arc-length, the knot vector is distributed according to the second derivative of the curve’s parameter respect to the curve’s arc-length and the control points and weights are optimized. Compared with the polynomial fitting method, the locality of the NURBS’ control points and the operating convenience of the NURBS make the fitting process more convenient and less parameter are required under same error requirement. Compared with online estimated second order Taylor expressed method, the proposed offline fitting NURBS interpolation method enhances the real time calculation efficiency and computation robustness and the feedrate fluctuation is decreased. The proposed offline NURBS fitting interpolation method is applied in an open motion controller to manufacture the freeform surface, which verify the validity and robustness of the interpolation method.Using the precision controlled B-spline fitting method, the five axis tool path is decoupled and fitted, the cutter-contact point’s arc-length based five axis tool path is obtained, which decreases the real time computation and increases the calculation efficiency of the feedrate scheduling. Due to the rotation axis of the five axis machining, the kinematic parameters of the each axes are coupling and nonlinear, which make the minimal time feedrate scheduling problem more difficult. Although real time feedrate scheduling methods and the RTCP function for the five axis are proposed in many advanced CNC, the feedrate only in trajectory system are considering. If the feedrate in the five axis machining are scheduling in real time, it is time consuming and low robustness. Therefore, the decoupling five axis tool path reconstitution method is proposed and the machining process of the five axis is scheduling based on the contract point’s arc-length five axis tool path. The simulation determines that the proposed method can make the machining process more rapid and stability.