Research Of Five-axis Tool Path Smoothing With Curvature Continuity And Its Interpolation Method

From the aerospace industries to the automotive and electronics industries, high-speed machining technology plays a pivotal role for curve and surface machining in modern manufacturing. Based on the simple, reliable and versatile algorithm, it is easy to describe curvilinear tool path by small short lines. Additionally, the adjustment of linear segments is convenient. As a result, it has a wide range of applications in high-speed machining field. However, the tangency and curvature discontinuities at the junctions of the linear segments would lead to a series of problems, such as fluctuation in feedrate, low processing efficiency, tool wear and tear, and deterioration of the surface quality. These disadvantages have been an obstacle to exploit the advantages in high speed machining, which cannot satisfy the growing requirements on high accuracy and quality.Curvature continuity, or G2 continuity, is the base for performing high-speed machining. In order to achieve on-line tool path smoothing, this dissertation proposes a real-time corner smoothing method with G2 continuity. Based on this smoothing method, a dynamic look-ahead algorithm which integrating the capability of tool path smoothing and speed planning over multi segments is presented. For the purpose of actual machining, this algorithm has been integrated into a CNC system with open architecture. The effectiveness and practicability of this method has been verified by simulation and practical manufacturing in three-axis and five-axis machining applications. The main work and the research results are listed in the following context:(1)Based on PH curves with G2 continuity, this dissertation proposes a corner smoothing method, which avoids the discontinuity of tangency and curvature in linear tool path containing plenty of short segments. And, the approximation errors can be restricted strictly when the corners are smoothed. This smoothing method has the following advantages: 1) the approximation errors have analytical relationship with transition lengths at the corner. This property facilitates the fast construction of the transition curve according to the predefined accuracy requirements, and contributes to the application of on-line tool path smoothing. 2) Due to the geometrical symmetry, the maximum curvature comes out in the middle point of the transition curve, which makes the determination of the feedrate constraints associated with the curvature conveniently. 3) Taking the advantages of PH curve that the curve length and its parameter have an analytical expression, the feedrate fluctuation can be eliminated in parameterization of tool path arc-length in interpolation. 4) This transition method can be applied in tool path smoothing both at two-dimension or and three-dimension cases.(2)After corner smoothing by the above method, the tool path have become a trajectory mixed up with lines and curves. A novel look-ahead algorithm is proposed which can make feedrate scheduling over multi segments for the soothed tool path. However, smoothed tool path does not mean smoothed motion, soft acceleration and deceleration, i.e. Acc & Dec, method is also a key point to achieve high-speed machining. Current existing soft Acc & Dec methods are described by piecewise functions, which have too much decision conditions. It would be inconvenient in the implementation of those Acc & Dec methods for their complexity. In this dissertation, an Acc & Dec method based on quintic polynomial curve is adopted. This method has a property called equal acceleration, which can give the analytical relationship between the displacement and velocity. Base on equal acceleration, we propose a new speed planning strategy, which can construct the speed profile according to the specific boundary conditions. In addition, the shape of the speed profile can be adjusted only by one parameter, which can be used to limit the maximum acceleration. According to the curvature distribution along the smoothed tool path, a serious of speed planning unit is established. And, the speed scheduling over multi segments is performed in the first unit. The application of speed planning unit contributes to the high efficiency in speed planning, and avoiding the fluctuation in feedrate. With the new segments come into the look-ahead buffer continuously, the speed profile can be updated dynamically. In comparison with the speed planning method without and with traditional look-ahead method, the time consuming in practical machining experiment reduced by 53.2% and 32.5%, respectively.(3)By establishing error mapping model of five-axis machine tools, the proposed tool path smoothing method is applied into the five-axis tool path soothing. The five-axis tool paths described in machine tool coordinate system(MCS) is defined by a series of discrete driving axes positions. The discontinuity in five-axis tool path is also an obstacle to achieve high speed five-axis machining. According to the difference in translational and rotational movements, five-axis tool path can be divided into two sub paths, and the dimensions in any one of those two sub paths is less than 3. By applying the corner smoothing method on the corners, the five-axis tool path can be smoothed. Different five-axis machine tool has different error mapping model. The error mapping model is established according to the kinematic characteristics of specific five-axis machine tool, which can supply the approximation error constraints for corner smoothing in sub tool paths. By taking the displacement of resultant movement in five-axis interpolation as synchronization parameter, monotonic cubic splines are employed to synchronize those two sub paths. The proposed look-ahead algorithm is also applicable to the interpolation of smoothed five-axis tool path, which contributes to the dramatic increase in feedrate. This smoothing and interpolation method is testified on an AC dual-table five axis machine tool for blade flank milling operation in semifinishing. The time consuming is only 31.67% in comparison with traditional look-ahead method. According to the kinematic characteristic of 3PRS mechanism, a homogeneous jacobian matrix is proposed, which is the foundation of error mapping model for 3PRS-XY hybrid mechanism. The same tool paths smoothing method is applied on the motion control of a 3PRS-XY experimental machine tool, which verify that this tool path smoothing method is suitable for different kinds of machines.(4)In work-piece coordinates system(WCS), by using a pair of quintic PH curves with G2 continuity, a smoothing method is proposed to round the corners in five-axis tool path. The five-axis tool path described in WCS contains tow trajectories, which stand for the movements of the tool tip and the second point on the tool axis, respectively. If those trajectories are described by linear segments, the problem of discontinuity in tangency and curvature will still occur. In order to smooth the tool path in WCS, there are two steps involved in this smoothing method. Firstly, according to the accuracy requirements of the tool tip contour and tool orientation tolerances, the corner is rounded with a pair of PH curves directly. Then, the control polygon lengths of PH curves are adjusted simply to guarantee the continuous variation of the tool orientation at the junctions between the transition curves and the remainder linear segments. Because the PH curves for corner rounding can be constructed without any iteration, and those two rounded trajectories are synchronized linearly in interpolation, which makes this smoothing method can be applied in a high efficiency way. Its high computational efficiency allows it to be implemented in real-time applications. This method has been integrated into a CNC system with an open architecture to implement real time smoothing for liner five-axis tool path. Simulations and experiments are conducted to validate practicability and reliability of this smoothing method.(5)A PC based CNC system with i MAC motion controller is constructed by integrating the tool path smoothing and speed scheduling algorithms. Taking an entire impeller machining as an example, the effectiveness of those algorithms and the practicability of the CNC system are verified. The data in CNC system are processed by a pipeline pattern, as a result, this CNC system has been divided into three basic modules, including HMI, numeric control kernel and motion control. The corresponding algorithms are integrated into the CNC system when those modules are developed. Finally, an entire impeller machining experiment, which includes rough milling, flank milling for blades and end milling for channel, is conducted to verify practicability of CNC system. In comparison with the tool paths described by G01 blocks, the proposed smoothing and interpolation methods in this dissertation have advantages in improving machining efficiency, maintaining accuracy and reducing time-consuming, which prove the effectiveness of those algorithms.