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Algorithm for Smooth S-curve Feedrate Profiling Generation 被引量:13
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作者 CHEN Youdong WEI Hongxing SUN Kai LIU Miao WANG Tianmiao 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2011年第2期237-247,共11页
The algorithms for feedrate profile generation,such as linear and S-curve profiles,have been widely used in machinery controllers,and these algorithms can greatly improve the smoothness of motion.However,most of the a... The algorithms for feedrate profile generation,such as linear and S-curve profiles,have been widely used in machinery controllers,and these algorithms can greatly improve the smoothness of motion.However,most of the algorithms lead to the discontinuous acceleration/deceleration and jerk,or high jerk levels,which is very harmful to machine tool or robot in most occasions. This paper presents a smooth S-curve feedrate profiling generation algorithm that produces continuous feedrate,acceleration,and jerk profiles.Smooth jerk is obtained by imposing limits on the first and second time derivatives of acceleration,resulting in trapezoidal jerk profiles along the tool path.The discretization of smooth S-curve feedrate is realized with a novel approach that improves the efficiency without calculating the deceleration point in each sampled time.To ensure that the interpolation time is a multiple of the value of sampled time,the feedrate,acceleration,jerk,and jerk derivative are recalculated.Meantime,to improve the efficiency,the interpolation steps of all regions are computed before interpolation.According to the distance of trajectory,the smooth S-curve acceleration and decelerations are divided into three blocks:normal block,short block type-Ⅰ,and short block type-Ⅱ.Finally feedrate discretization of short block type-Ⅰand type-Ⅱis obtained with considering the efficiency.The proposed generation algorithm is tested in machining a part on a five axis milling machine,which is controlled with the CNC system for newly developed high-speed machine tools.The test result shows that the smooth S-curve approach has the smoother feedrate,acceleration,deceleration,and jerk profiles than S-curve.The proposed algorithm ensures the automated machinery motion smoothness,and improves the quality and efficiency of the automated machinery motion planning. 展开更多
关键词 S-curve acceleration/deceleration feedrate control computer numerical control(CNC)
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Improved time-optimal B-spline feedrate scheduling for NURBS tool paths in CNC machining
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作者 Yang Li Fu-Sheng Liang +1 位作者 Lei Lu Cheng Fan 《Advances in Manufacturing》 SCIE EI CAS CSCD 2023年第1期111-129,共19页
Feedrate scheduling in computer numerical control(CNC)machining is of great importance to fully develop the capabilities of machine tools while maintaining the motion stability of each actuator.Smooth and time-optimal... Feedrate scheduling in computer numerical control(CNC)machining is of great importance to fully develop the capabilities of machine tools while maintaining the motion stability of each actuator.Smooth and time-optimal feedrate scheduling plays a critical role in improving the machining efficiency and precision of complex surfaces considering the irregular curvature characteristics of tool paths and the limited drive capacities of machine tools.This study develops a general feedrate scheduling method for non-uniform rational B-splines(NURBS)tool paths in CNC machining aiming at minimizing the total machining time without sacrificing the smoothness of feed motion.The feedrate profile is represented by a B-spline curve to flexibly adapt to the frequent acceleration and deceleration requirements of machining along complex tool paths.The time-optimal B-spline feedrate is produced by continuously increasing the control points sequentially from zero positions in the bidirectional scanning and sampling processes.The required number of knots for the time-optimal B-spline feedrate can be determined using a progressive knot insertion method.To improve the computational efficiency,the B-spline feedrate profile is divided into a series of independent segments and the computation in each segment can be performed concurrently.The proposed feedrate scheduling method is capable of dealing with not only the geometry constraints but also high-order drive constraints for any complex tool path with little computational overhead.Simulations and machining experiments are conducted to verify the effectiveness and superiorities of the proposed method. 展开更多
关键词 B-spline feedrate Non-uniform rational B-splines(NURBS)tool path Knot insertion Bidirectional scanning Computer numerical control(CNC)machining
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Jerk-limited feedrate scheduling and optimization for five-axis machining using new piecewise linear programming approach 被引量:8
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作者 SUN YuWen CHEN ManSen +2 位作者 JIA JinJie LEE Yuan-Shin GUO DongMing 《Science China(Technological Sciences)》 SCIE EI CAS CSCD 2019年第7期1067-1081,共15页
In this paper, a new computation method and an optimization algorithm are presented for feedrate scheduling of five-axis machining in compliance with both machine drive limits and process limits. Five-axis machine too... In this paper, a new computation method and an optimization algorithm are presented for feedrate scheduling of five-axis machining in compliance with both machine drive limits and process limits. Five-axis machine tool with its ability of controlling tool orientation to follow the sculptured surface contour has been widely used in modern manufacturing industry. Feedrate scheduling serving as a kernel of CNC control system plays a critical role to ensure the required machining accuracy and reliability for five-axis machining. Due to the nonlinear coupling effects of all involved drive axes and the saturation limit of servo motors, the feedrate scheduling for multi-axis machining has long been recognized and remains as a critical challenge for achieving five-axis machine tools’ full capacity and advantage. To solve the nonlinearity nature of the five-axis feedrate scheduling problems, a relaxation mathematical process is presented for relaxing both the drive motors’ physical limitations and the kinematic constraints of five-axis tool motions. Based on the primary optimization variable of feedrate, the presented method analytically linearizes the machining-related constraints, in terms of the machines’ axis velocities, axis accelerations and axis jerks. The nonlinear multi-constrained feedrate scheduling problem is transformed into a manageable linear programming problem. An optimization algorithm is presented to find the optimal feedrate scheduling solution for the five-axis machining problems. Both computer implementation and laboratorial experiment testing by actual machine cutting were conducted and presented in this paper. The experiment results demonstrate that the proposed method can effectively generate efficient feedrate scheduling for five-axis machining with constraints of the machine tool physical constraints and limits. Compared with other existing numerical methods, the proposed method is able to find an accurate analytical solution for the nonlinear constrained five-axis feedrate scheduling problems without compromising the efficiency of the machining processes. 展开更多
关键词 FIVE-AXIS MACHINING feedrate SCHEDULING JERK LINEAR PROGRAMMING optimization
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Path,feedrate and trajectory planning for free-form surface machining:A state-of-the-art review 被引量:9
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作者 Yuwen SUN Jinjie JIA +2 位作者 Jinting XU Mansen CHEN Jinbo NIU 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2022年第8期12-29,共18页
Nowadays,free-form surfaces have been widely used in various industrial fields.They are usually machined by CNC machine tools,but recently have also begun to be manufactured by industrial robotic arm manipulators,than... Nowadays,free-form surfaces have been widely used in various industrial fields.They are usually machined by CNC machine tools,but recently have also begun to be manufactured by industrial robotic arm manipulators,thanks to low cost,large operation reaching space and high machining flexibility of robot.So far,various methodologies have been proposed to improve efficiency and quality of free-form surface machining,thus this paper aims at providing a state-ofthe-art review on research advances in free-form surface machining.In this review,tool path generation,feedrate scheduling in Cartesian space and trajectory planning in joint space are focused for both CNC machining and robot machining,and their research statues,existing difficulties and key issues are discussed in detail.Finally,the feasible routes,breakthrough points and future development trend are also expounded. 展开更多
关键词 CNC machining feedrate Free-form surface Robotic machining Tool path TRAJECTORY
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Feedrate scheduling method for constant peak cutting force in five-axis flank milling process 被引量:6
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作者 Liping WANG Xing YUAN +1 位作者 Hao SI Feiyu DUAN 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2020年第7期2055-2069,共15页
It is extremely important to select appropriate feedrates for the stable machining of parts with ruled surface in modern aviation industrial applications.However,the current studies take too much time to achieve this ... It is extremely important to select appropriate feedrates for the stable machining of parts with ruled surface in modern aviation industrial applications.However,the current studies take too much time to achieve this goal.Therefore,this paper presents an efficient feedrate optimization method for constant peak cutting force in five-axis flank milling process.The solution method of the instantaneous undeformed chip thickness(IUCT)is proposed using least squares theory with the cutter entry angle and feedrate as variables.Based on this method,an explicit analytical expression of the peak cutting force for each cutting point is established.Furthermore,a feedrate scheduling method is developed to quickly solve the appropriate feedrate under constant peak cutting force.To verify the proposed IUCT model,the fitting IUCT is compared with the accuracy data at different feedrates.Additionally,some experiments of five-axis flank milling are conducted to demonstrate the effectiveness of the peak force model and the feedrate scheduling method.And the surface roughness before and after feedrate scheduling is detected.The results show that the proposed feedrate scheduling method can quickly adjust the feedrate and ensure constant peak force during machining.At the same time,the surface quality is kept at a high level. 展开更多
关键词 Cutter runout feedrate scheduling Force control Instantaneous undeformed chip thickness Peak cutting force
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Time Optimal Feedrate Generation with Confined Tracking Error Based on Linear Programming 被引量:4
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作者 GUO Jianxin ZHANG Qiang +1 位作者 GAO Xiao-Shan LI Hongbo 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2015年第1期80-95,共16页
In this paper,the problem of time optimal feedrate generation under confined feedrate,axis accelerations,and axis tracking errors is considered.The main contribution is to reduce the tracking error constraint to const... In this paper,the problem of time optimal feedrate generation under confined feedrate,axis accelerations,and axis tracking errors is considered.The main contribution is to reduce the tracking error constraint to constraints about the axis velocities and accelerations,when the tracking error satisfies a second order linear ordinary differential equation.Based on this simplification on the tracking error,the original feedrate generation problem is reduced to a new form which can be efficiently solved with linear programming algorithms.Simulation results are used to validate the methods. 展开更多
关键词 CNC machining dynamics linear programming optimal control time optimal feedrate planning tracking error.
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VARIABLE FEEDRATE INTERPOLATION OF NURBS TOOLPATH WITH GEOMETRIC AND KINEMATICAL CONSTRAINTS FOR FIVE-AXIS CNC MACHINING 被引量:1
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作者 SUN Yuwen ZHOU Jianfeng GUO Dongming 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2013年第5期757-776,共20页
Variable feedrate interpolation algorithms for five-axis parametric toolpath are very promising but still rather limited currently.In this paper,an off-line feedrate scheduling method of dual NURBS curve is presented ... Variable feedrate interpolation algorithms for five-axis parametric toolpath are very promising but still rather limited currently.In this paper,an off-line feedrate scheduling method of dual NURBS curve is presented with geometric and kinematical constraints.For a given dual parametric curve,the feedrates of sampling points are first scheduled sequent with confined feedrate of cutter tip and machine pivot,chord error,normal acceleration and angular feedrate.Then,the feedrate profiles of angular feed acceleration sensitive regions of the path are adjusted using a bi-directional scanning algorithm.After that,a linear programming method is used to adjust the feedrate profiles of linear feed acceleration sensitive regions and control the linear feed acceleration of both cutter tip and machine pivot within preset values.Further,a NURBS curve is used to fit the feedrates of sampling points.Finally,illustrative examples are carried out to validate the feasibility of the proposed feedrate scheduling method.The results show that the proposed method has the ability of effectively controlling the angular feed characters of cutter axis as well as the chord error and linear feed characters of cutter tip and machine pivot,and it has potential to be used in high accuracy and high quality five-axis machining. 展开更多
关键词 feedrate interpolation five-axis machining NURBS tool path.
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High Accurate Interpolation of NURBS Tool Path for CNC Machine Tools 被引量:11
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作者 LIU Qiang LIU Huan YUAN Songmei 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2016年第5期911-920,共10页
Feedrate fluctuation caused by approximation errors of interpolation methods has great effects on machining quality in NURBS interpolation, but few methods can efficiently eliminate or reduce it to a satisfying level ... Feedrate fluctuation caused by approximation errors of interpolation methods has great effects on machining quality in NURBS interpolation, but few methods can efficiently eliminate or reduce it to a satisfying level without sacrificing the computing efficiency at present. In order to solve this problem, a high accurate interpolation method for NURBS tool path is proposed. The proposed method can efficiently reduce the feedrate fluctuation by forming a quartic equation with respect to the curve parameter increment, which can be efficiently solved by analytic methods in real-time. Theoretically, the proposed method can totally eliminate the feedrate fluctuation for any 2nd degree NURBS curves and can interpolate 3rd degree NURBS curves with minimal feedrate fluctuation. Moreover, a smooth feedrate planning algorithm is also proposed to generate smooth tool motion with considering multiple constraints and scheduling errors by an efficient planning strategy. Experiments are conducted to verify the feasibility and applicability of the proposed method. This research presents a novel NURBS interpolation method with not only high accuracy but also satisfying computing efficiency. 展开更多
关键词 NURBS INTERPOLATION feedrate machine tool CNC
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Study on Real-time Look-ahead and Adaptive Parametric Curve Interpolator 被引量:2
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作者 郭伟 杜道山 +1 位作者 徐荣珍 李从心 《Journal of Shanghai Jiaotong university(Science)》 EI 2007年第3期388-393,共6页
The principle of real-time look-ahead was introduced and analysed. An adaptive parametric curve interpolator with a real-time look-ahead function was developed for non-uniform rational B-spline (NURBS) curves interpol... The principle of real-time look-ahead was introduced and analysed. An adaptive parametric curve interpolator with a real-time look-ahead function was developed for non-uniform rational B-spline (NURBS) curves interpolation, which considering the maximum acceleration/deceleration of the machine tool. In order to deal with the acceleration/deceleration around the feedrate sensitive corners, the look-ahead function was designed and illustrated. It can detect and adjust the feedrate adaptively. With the help of real-time look-ahead, the acceleration/deceleration can be limited to the range of the machine tool capacity. Thus, feedrate fluctuation is reduced. A NURBS curve interpolation experiment was provided to verify the feasibility and advantages of the proposed interpolator with a real-time look-ahead function. 展开更多
关键词 adaptive interpolator LOOK-AHEAD non-uniform rational B-spline curves feedrate sensitive corner chord error
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Adaptation of feed rate for 3-axis CNC high-speed machining 被引量:1
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作者 张得礼 周来水 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2009年第3期391-395,共5页
To improve the efficiency of CNC machining, assumptive transit circular arc is used to contour two adjacent moves together on the comer to make smooth paths. The radios of transit circular arc can be adjusted with con... To improve the efficiency of CNC machining, assumptive transit circular arc is used to contour two adjacent moves together on the comer to make smooth paths. The radios of transit circular arc can be adjusted with contour accuracy, and the feed rate on the corner can be controlled through limiting the maximum feed rate of transit circular arc segment. A look-ahead algorithm for a series of moves is proposed for speed adjustment in advance, which avoids the occurrence of overload of cutting tool on the comer and reduces the servo track error of parts on the corner or of circular arc move. Equivalent trapezoidal velocity profile is used to analyze the speed of S-curve velocity profile and work out its accurate interpolation, which overcomes the disadvantage of looking up table to calculate feed rate approximately, hence high accuracy and fine surface quality can be obtained while the machining speed is high. The proposed methods can meet the requirements of real-time analysis of high-speed machining. The presented algorithm is effective and has been adopted by CNC system of newly developed high-speed milling machine. 展开更多
关键词 CNC feedrate smoothing S-curve velocity profile high-speed machining
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High speed interpolation for micro-line trajectory and adaptive real-time look-ahead scheme in CNC machining 被引量:18
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作者 ZHANG LiXian SUN RuiYong +1 位作者 GAO XiaoShan LI HongBo 《Science China(Technological Sciences)》 SCIE EI CAS 2011年第6期1481-1495,共15页
CNC machining plays an important role in mechanical manufacturing.A key issue is to improve the machining feedrate while keeping the machining precision and satisfying the acceleration constraints of the CNC machine.F... CNC machining plays an important role in mechanical manufacturing.A key issue is to improve the machining feedrate while keeping the machining precision and satisfying the acceleration constraints of the CNC machine.For the consecutive micro-line segments interpolation,the velocities at the junction of two segments are the bottlenecks for the machining efficiency.This paper proposes a multi-period turning method to improve the feedrate at the junctions using the linear acceleration and deceleration mode,which utilizes the maximal acceleration capabilities of the NC machine while satisfying the machining precision.A new and more efficient look-ahead method and a feedrate override method are also proposed to boast the global machining speed.The proposed algorithm has been implemented on Blue Sky NC System,and experimented in real material manufacturing.Compared with several existing algorithms,the current algorithm can improve the manufacturing time ranging from 50% to 180%,depending on the machining parameters,and also results in better machining quality.In addition,the algorithm also satisfies the need of real-time interpolation. 展开更多
关键词 CNC micro-line segment multi-period turning look-ahead scheme real-time interpolation feedrate override
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Micro ball-end milling of freeform titanium parts 被引量:1
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作者 Ali Mamedov Ismail Lazoglu 《Advances in Manufacturing》 SCIE CAS CSCD 2015年第4期263-268,共6页
Micro machining has growing number of applications in various industries such as biomedical, automotive, aerospace, micro-sensor, micro-actuator and jewelry industries. Small-sized freeform titanium parts are frequent... Micro machining has growing number of applications in various industries such as biomedical, automotive, aerospace, micro-sensor, micro-actuator and jewelry industries. Small-sized freeform titanium parts are frequently needed in the biomedical applications, especially in the implantations such as mini-blood pumps and mini left-ventricular assist devices, finger joint replacements and small bone implants. Most of the small-sized titanium parts with freeform geometries are machined using micro ball-end milling before polishing and other surface treatments. Decreasing the cycle time of the machining parts is important for the productivity. In order to reduce the cycle time of the roughing process in the micro ball-end milling, this paper investigates the imple- mentation of a previously developed force-based feedrate scheduling (FFS) technique on micro milling of freeform titanium parts. After briefly introducing the instantaneous micro milling forces in micro ball-end milling of titanium parts with freeform surfaces, the FFS technique is implemented in the rough machining of a freeform titanium surface to demonstrate the cycle time reduction potentials via virtual micro milling simulations. 展开更多
关键词 Micro milling Roughing - feedrate scheduling - Force model - Titanium - Ti-6Al-4V
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