Research On Trajectory Planning And Chatter Stability Of Robotic Milling

The advancement and application of industrial robot technology is an important parts of intelligent manufacturing in China.And the industrial robot has become an indispensable core equipment in automated production lines.In recent years,the robot cutting system,which takes the industrial robot especially the six degree-of-freedom(DOF)robot as the main body of motion and equips high speed electric spindle at the end,has been rapidly developed in the field of metal cutting.Compared with the traditional compute numerical control(CNC)machine tools,robot cutting has the advantages of low cost,large working space,good space accessibility and high flexibility.It is especially suitable for complex surface machining with large size,low cutting force and low precision requirement.Compared with robot polishing,grinding and drilling process,robotic milling is more difficult and has not been widely used,which has gotten the most attention of researchers.Vibration is the main factors limiting the application of robotic milling.There are many reasons for the cutting vibration,including vibration caused by unsmooth machining trajectory and chatter due to low stiffness.Milling with the serial robots,the open-chain multi-rod structure and the weak stiffness have an amplification effect on the vibration of each joint,which tends to cause large fluctuations at the end,and requires higher smooth trajectory control.At the same time,the weak stiffness causes the robot processing system to have low tolerance to the working load,and the chatter phenomenon is more likely to occur under the milling force,which seriously affects the machining accuracy and surface quality.Therefore,the research on the trajectory planning(including the path planning and federate scheduling)and chatter stability analysis,which can fundamentally reduce the vibration caused by trajectory control and guide the selection of machining parameters,is of great significance for promoting the application of robotic milling.This paper focus on the six DOF robotic milling system and conducts research on trajectory planning and chatter stability analysis to improve the motion smoothness,explore the dynamic characteristic of cutting system and give the guidance for selection of cutting parameters.The main contents are as follows:(1)The problem of redundant DOF in the path planning of robotic milling is studied where an optimized redundant planning method based on segmented global optimization strategy is proposed.Firstly,the singularity and stiffness of robot are considered and the weighted comprehensive performance index is defined.Meanwhile,the joint-limit is used as a judgment condition which considers the joint-limit constraints at the middle points.Then,the segmented global optimization strategy is proposed where the whole path is segmented and each segment is the optimization planning unit.In addition,a new method for giving the displacement constraint of the redundant DOF is also proposed.Finally,the planning method for redundant DOF based on the comprehensive index and segmented global optimization strategy is generated,which can improve planning results.(2)The federate scheduling considering round-off error is studied where a bidirectional-time-rounding-based federate scheduling method is proposed.Firstly,the characteristics of S-shaped acceleration/deceleration(ACC/DEC)algorithm is analyzed and some monotonic properties are discovered between jerk,time and displacement.Based on these monotonic properties,a time-rounding-up-based federate scheduling scheme is proposed,which is suitable for most of situations and can limit the motion parameters within their given ranges to guarantee the motion smoothness.Then,for the case where the above method is not applicable,a time-rounding-down-based federate scheduling method with round-off error compensation is proposed,which can reduce the rounding time and the corresponding round-off error.Meanwhile,the continuous of acceleration profile can be guaranteed after the round-off error compensation.Finally,the bidirectional-time-rounding-based federate scheduling method is generated by combining these two methods,which can adapt to any situation and form strong constraints on various parameters to guarantee the motion smoothness.(3)The federate scheduling for NURBS curve is studied where a bidirectional adaptive federate scheduling method is proposed based on S-shaped ACC/DEC algorithm Firstly,based on the fundamental of S-shaped algorithm,an adaptive federate scheduling method is designed,which can improve the scheduling accuracy.Then,to consider the multiple federate constraints in the end point area on both sides of the curve segment,a bidirectional interpolation strategy including the adaptive task scheduling method and the meeting processing method is proposed,which can guarantee that the interpolation of a NURBS curve can be conducted in two directions simultaneously and orderly and improve the scheduling accuracy.Meanwhile,the round-off error is also considered in the bidirectional interpolation to guarantee the motion smoothness.(4)The robot ACC/DEC algorithm is studied where a jerk-continuous ACC/DEC algorithm is proposed based on the polynomial and trigonometric functions to further improve the motion smoothness.Firstly,polynomial and trigonometric functions are used to construct the jerk profile,which can maintain the maximum jerk and acceleration.Therefore,the smooth trajectory can be generated with higher motion efficiency.Then,a proportional construction method is proposed to determine the relation between polynomial and trigonometric part,which can reduce the number of independent variables and the computational load of federate.The configurability of the proportional parameter also increased the flexibility.Finally,the federate scheduling method based on the proposed ACC/DEC algorithm is given.Meanwhile,the round-off error is also considered with the simplified ACC/DEC algorithm to maintain the continuous jerk.(5)The dynamic characteristics and chatter stability of the robotic milling system is studied.Firstly,the planar multi DOF dynamic model in physical space and the cutting force model are established.Then,based on the non-symmetric complex modal theory and the experimental modal analysis method,the modal analysis experiment is conducted.And the various modal parameters can be identified.Based on the modal parameters,the milling dynamic model can be reconstructed in modal space.Finally,the semi-discrete method is used for milling stability analysis.The stability lobe is drawn and validated by milling experiment.