Elastodynamic Modeling And Cutting Performance Analysis Of A Novel 5-DOF Hybrid Robot

Driven by many practical needs for on-site manufacturing of large and complex structural components,this dissertation first investigates the elastodynamic modeling and chatter stability of a novel 5-DOF(degrees of freedom)hybrid robot known as Tri Mule.This is followed by the study of the 3D surface topography generation and representation of machined surface to evaluate the milling quality of the Tri Mule robot.Finally,experimental studies are carried out as verifications.The following contributions have been made.By taking the Tri Mule robot as an example,an effective semi-analytical approach for predicting the full set of lower-order dynamics using a minimum set of generalized coordinates is proposed.In this method,super-element models of limbs are first established by substructure synthesis technique to reduce the DOF of the FE(finite element)model while ensuring high accuracy.Then,a general and comprehensive stiffness model of passive joints,which are commonly used in the parallel mechanism having closed loops,is derived using reciprocal/dual properties of twist/wrench system.This model extremely simplifies the assembly of substructures.Both simulation and experimental results on a prototype machine show that the semi-analytical model enables the lower-order dynamic behaviors of the robot over entire workspace to be predicted with sufficient accuracy and efficiency.The former is in good agreement with the latter in terms of natural frequencies,mode shapes,and FRFs(frequency response functions)at TCP(tool center point).In addition,the first order bending modes of actuated limbs should be fully considered in the modeling due to their impact on lower-order dynamic behaviors at TCP.The proposed model lays a solid ground for the prediction of the milling stability and the 3D surface topography.Based on the dynamic model of the robot system considering the tool and tool holder,the dynamic milling process equations containing regenerative and mode coupling effects are derived.This is followed by investigations of milling stability of the Tri Mule robot using two different methods,i.e.,zero order approximation(ZOA)and improved full-discretization method(IFDM).The analytical expression of the limit stable depths of cut can be directly derived by the ZOA method.In the IFDM,sparse matrix multiplication operations are applied to improve the computational efficiency.Both simulation and experimental results on a prototype machine show that the stability is dominated by the pose-independent higher-order dynamics of the robot in high speed and large radial immersion milling of the Aluminium alloy;and dominated by the pose-dependent lower-order dynamics in low speed and small radial immersion milling of the Titanium alloy.In addition,the measured states of cutting tests at two different conditions are in good agreement with the predicted results.The proposed models and methods are able to reveal the variations of the milling stability with configurations,which offers a useful guideline for realizing stable milling of the Tri Mule robot.Based upon the analysis of the force and vibration at different positions of the cutter,the analytical expressions of tool motion trajectories considering the influence of robot dynamics are first derived.Then,an accurate numerical algorithm is proposed to solve the surface profile,and to construct the 3D surface topography by using Newton iteration method.In this algorithm,the initial value of the iteration can be reasonably set by using the theorem of zero existence of closed interval continuous function with sufficient accuracy.Both simulation and experimental results on a prototype machine show that the surface location error and roughness are closely related to the pose-dependent lower-order dynamics of the robot in low speed and small radial immersion milling of the Titanium alloy.The maximum deviations between predicted and measured values are about 18% and 15%.The simulation results also show that distributions of the mean surface location error and mean square error of the roughness are proportional to the maximum dynamic compliance of the lower-order modes.The proposed models and methods are able to reveal the variations of surface topography characteristics with configurations and cutting parameters,providing an effective technical means for the objective evaluation of the milling quality of the Tri Mule robot.The outcomes of this dissertation not only offer a technical support for high performance milling of the Tri Mule robot,but also lay a solid foundation for its engineering applications.