Time-Optimal Feedrate Planning for Freeform Toolpaths for Manufacturing Applications

Trajectory Optimization;CNC

Chen, Christina (Qing Ge)advisor:Erkorkmaz, Kaan ; affiliation1:Faculty of Engineering ; Erkorkmaz, Kaan ;

University of Waterloo

关键词: Trajectory Optimization;    Master Thesis;    CNC;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/13040/3/Chen_ChristinaQingGe.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

Optimality and computational efficiency are two desired yet competing attributes of time-optimalfeedrate planning. A well-designed algorithm can vastly increase machining productivity,by reducing tool positioning time subject to limits of the machine tool and process kinematics. Inthe optimization, it is crucial to not overload the machining operation, saturate the actuators’ limits,or cause unwanted vibrations and contour errors. This presents a nonlinear optimization problemfor achieving highest possible feedrates along a toolpath, while keeping the actuator level velocity,acceleration and jerk profiles limited. Methods proposed in literature either use highly elaboratenonlinear optimization solvers like Sequential Quadratic Programming (SQP), employ iterativeheuristics which extends the computational time, or make conservative assumptions that reducescalculation time but lead to slower tool motion.This thesis proposes a new feedrate optimization algorithm, which combines recasting of theoriginal problem into a Linear Programming (LP) form, and the development of a new windowingscheme to handle very long toolpaths. All constraint equations are linearized by applying B-splinediscretization on the kinematic profiles, and approximating the nonlinear jerk equation with alinearized upper bound (so-called 'pseudo-jerk’). The developed windowing algorithm first solvesadjacent portions of the feed profile with zero boundary conditions at overlap points. Afterwards,using the Principle of Optimality, connection boundary conditions are identified that guarantee afeasible initial guess for blending the pre-solved adjacent feed profiles into one another, through aconsecutive pass of LP.Experiments conducted at the sponsoring company of this research, Pratt & Whitney Canada(P&WC), show that the proposed algorithm is able to reliably reduce cycle time by up to 56% and38% in two different contouring operations, without sacrificing dynamic positioning accuracy.Benchmarks carried out with respect to two earlier proposed feedrate optimization algorithms,validate both the time optimality and also drastic (nearly 60 times) reduction in the computationalload, achieved with the new method. Part quality, robustness and feed drive positioning accuracyhave also been validated in 3-axis surface machining of a part with 1030 waypoints and 10,000constraint checkpoints.