| dc.description.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. | en |
