Time-optimal, minimum-jerk, and acceleration continuous looping and stitching trajectory generation for 5-axis on-the-fly laser drilling

Highlights

• Novel idea of applying optimized trajectories for laser drilling passes.

• Developed algorithms have been applied on gas turbine combustion chamber panels.

• Proposed technique provides over 6% reduction in cycle time.

• 56% reduction in the integral square of jerk as been achieved (vibration reduction).

• Minimization in vibrations on laser optics significantly reduced.

Abstract

The process of on-the-fly laser drilling is capable of achieving high throughputs and offers a highly productive approach for producing pre-defined groups of holes (clusters) to be laser drilled on freeform surfaced parts. On-the-fly drilling also presents different technological requirements, needing a different kind of trajectory optimization solutions. Current machine tool controllers are not equipped with appropriate trajectory functions that can take full advantage of the achievable laser drilling speeds. This paper presents the novel idea of applying optimized looping and stitching trajectories (by solving for time optimal trajectories for individual machine axis and choosing the minimum value of the integral square of jerk) for looping a cluster during multiple laser drilling passes, or making a connection between consecutive clusters with given position and velocity boundary conditions. While finding the minimal motion cycle time and minimizing vibrations transmitted to the laser optics causing misalignment (requiring significant manufacturing stoppage for optics realignment). The produced smooth and time optimal trajectories, hand-in-hand with cluster trajectory optimization, proved to reduce both the total drilling cycle time and vibrations transmitted through 5-axis machine to the laser optics. In detail, when compared to currently used on-the-fly drilling methods in industry today (Ex. at Pratt and Whitney Canada), ∼6% reduction in overall cycle time was observed for specific part examples due to the avoidance of unnecessary accelerations and decelerations between hole locations. In individual connecting trajectory instances within part drilling process, up to ∼62% connection time reduction was observed. Furthermore, a substantial improvement of up to ∼56% increase in the motion smoothness compared to using direct linear interpolation between the target hole locations due to abrupt start-stop motions between consecutive clusters and before repeated drilling of the same cluster.

Introduction

Current machine tool controllers are not equipped with the appropriate on-the-fly laser drilling trajectory functions that can take full advantage of the achievable laser drilling speeds, although the process provides highly productive methods for producing hole clusters and is capable of achieving high throughputs. Refs. [1], [2] present a novel and time-optimized trajectory generation algorithm which addresses this problem. This paper details the derivation (generation) and optimization of the looping and stitching component of the 5-axis on-the-fly laser drilling process targeting both, production cycle time and machine vibration minimization.

The hole locations (to be laser drilled) are provided as pre-programmed sequences by the Computer Aided Design/Manufacturing software (CAD/CAM). A time-optimized trajectory for each sequence is planned through a series of time-scaling and unconstrained optimization operations, which guarantees a feasible solution [1], [2]. The initial guess for this algorithm is obtained by minimizing the integral square of the fourth time derivative (i.e. ‘snap’). The optimized trajectories for each cluster are then joined together or looped onto themselves (for repeated laser shots) using a time-optimized looping/stitching (optimized/smooth toolpath to repeat/loop a cluster or connect/stitch between consecutive clusters) algorithm. This algorithm also minimizes the integral square of jerk in the faster axes.

The motion duration between consecutive holes (especially for on-the-fly laser drilling) to be kept constant and minimized. This corresponds to the laser pulsing period of the drilling machine.

Between the locations of the holes, the laser focal point motion trajectory can be modulated and is not fixed, which helps achieve the maximum possible time reduction.

Fig. 1 shows a 5-axis laser drilling setup actuated by direct drive motors. Linear motors are used for motion in the x-, y-, and z-axes directions, and the trunion has a formation with two rotary axes (for rotary motions in the a- and c-axes). This machine was built for drilling gas turbine combustion chamber panel hole patterns like the one shown in Fig. 2. Fig. 2 also shows the numbered collections or groups of holes (clusters) that need to be drilled, in this specific example; there are 12 different clusters to be drilled by means of an optimized smooth trajectory. It is obvious that on-the-fly drilling of such a pattern requires full coordination of all 5-axes. Each cluster (or group of holes) needs to be drilled at a fixed laser pulsing frequency. After drilling a single cluster the connection between the groups of holes (clusters) also has to be seamless with continuous smooth motion instead of decelerating and stopping at end of one cluster, repositioning at the beginning of the next cluster and accelerating at start of the drilling process for the consecutive clusters. The seamless cluster connection is performed in order to avoid unwanted vibrations on the laser optics and the 5-axis machine induced by aggressive and repetitive stopping and starting motions during the process. Hence, the key to achieving high productivity in this operation is minimizing the duration of both cluster drilling and repositioning, while respecting the physical limitations of the machine and process.

Currently, there exists no commercial interpolator or published technique prior to Ref. [2], [3] including this study, which generates time-optimized trajectories for on-the-fly (and percussion) laser drilling.

Therefore, this paper presents a stitching algorithm for looping the same cluster trajectory (for multiple drilling passes) and stitching between consecutive clusters. For point to point motion the ‘s-curve’ profile shown in Fig. 3 is known to be the time-optimal one. Here, this approach has been adopted with some modification, which generates the quickest possible motion for each axis with guaranteed kinematic feasibility, as presented in Section 3. Then, all axes need to be synchronized so that the total motion duration is equal to that of the slowest axis, and an integer multiple of the laser pulsing period, which is explained in Section 4. This is done to avoid turning the laser off while repositioning the beam, which can result in for tens of seconds delay in the laser control circuitry. Instead, a quick shutter is used in the optics path, which diverts the beam away from the workpiece. Slowing down the profiles in the faster axes allows for a wide range of feasible solutions to choose from, which is utilized to the advantage of reducing the vibrations induced by minimizing the motion jerk in the individual axes, as explained in Section 5. The trajectories that are planned for each axis with different switching times are then assembled and re-parameterized, so they can be executed as a single continuous stream. Details of this step are presented in Section 6, which also shows a sample result for the overall stitching algorithm developed in this paper. Finally, the conclusions are presented in Section 7.

The idea of looping and stitching is to make a seamless connection with given position and velocity boundary conditions while finding the minimal motion cycle time. This is used for looping a cluster during multiple laser drilling passes, or making a connection between consecutive clusters in the part program. In this paper, a procedure is presented that first solves the time-optimized trajectory for each axis, and then synchronizes the total motion duration among multiple axes by slowing down the faster axes to accommodate the slowest one(s). While doing so, the kinematic solutions for the faster axes are also optimized to minimize the integral square of jerk. Fig. 4 shows how looping and stitching trajectories are used.