Time-optimal interpolation for five-axis CNC machining along parametric tool path based on linear programming

A smooth curve evolution approach to the feedrate planning on five-axis toolpath with geometric and kinematic constraints

“…For a target feedrate profile, the ND constraints, namely axial accelerations A u a j ( ) and jerks J u a j ( ) or/ and tangential acceleration a u j ( ) and jerk J u j ( ) , are evaluated at each sampling position u j on the path curve C u ( ). Generally, the acceleration and jerk constraints can be analytically got using Formula (12) and (14), but it is complicated in calculation and thus is often solved using a numerical method. From Eq.…”

“…Li et al [11] presented a NURBS preinterpolator with the converter function of linear/circular segments for a CNC system, so that the NURBS interpolator can be thoroughly applied for five-axis machining. More recently, in order to confine the axis accelerations and jerks, the feedrate optimization modes have respectively established using linear programming and sequential quadratic programming methods [12,13], from which the feedrate profile of cutter tip can be directly obtained once the concrete machine configuration is given in advance. Based on the 5-axis toolpath represented by two B-spline curves, Beudaert et al [14,15] built a 5-axis corner rounding model to smooth the tool path geometry, which is suitable for acceleration and jerk limited feedrate interpolation.…”

Minimum Time Trajectory Optimization of CNC Machining with Tracking Error Constraints

“…Here we define a typical problem named as original P, which is described as minimum motion time along given path while the trajectory is only subjected to velocity and acceleration constraints. According to the works of Bobrow et al [27], Zhang et al [11], and Fan et al [12], we have the fact that the optimal solution of the original P is maximum among all (17), which is also feasible for the original P, and then we have…”

“…Zhang and Li [11] presented a convex optimization approach to solve the jerk constrained minimum time trajectory planning problem. Then a linear programming method was shown in Fan et al [12] to obtain smooth trajectory.…”

Speed Control in Numeric Controlled System

“…Solving nonlinear programming problems result with large computational time. Fan et al [1] proposes another discretization approach, and linearization of the problem, transforming it into linear programming problem, which has predictable computational time.…”