Time-Optimal Feedrate Planning for Freeform Toolpaths for Manufacturing Applications

Abstract

Optimality and computational efficiency are two desired yet competing attributes of time-optimal feedrate 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. In the 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 problem for 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 elaborate nonlinear optimization solvers like Sequential Quadratic Programming (SQP), employ iterative heuristics which extends the computational time, or make conservative assumptions that reduces calculation time but lead to slower tool motion. This thesis proposes a new feedrate optimization algorithm, which combines recasting of the original problem into a Linear Programming (LP) form, and the development of a new windowing scheme to handle very long toolpaths. All constraint equations are linearized by applying B-spline discretization on the kinematic profiles, and approximating the nonlinear jerk equation with a linearized upper bound (so-called ‘pseudo-jerk’). The developed windowing algorithm first solves adjacent 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 a feasible initial guess for blending the pre-solved adjacent feed profiles into one another, through a consecutive 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% and 38% 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 computational load, achieved with the new method. Part quality, robustness and feed drive positioning accuracy have also been validated in 3-axis surface machining of a part with 1030 waypoints and 10,000 constraint checkpoints.