<br> [MAS.865](../..) &gt; [Path Planning](..) &gt; Toolpath Optimization ## Toolpath Optimization <div style="margin-left:2.5%"> ### Default Machining Strategies The simplest approach that "just works" but does not necessarily optimize the toolpath is to cover the surface using either its parameterization, or some sort of regular pattern overlaid onto the geometry (e.g. by intersecting planes). These are the two most common variants, also known as: * Iso-parametric curves (parametric N-D curves with N-1 parameters kept constant), and * Iso-planar curves (intersection curves with a family of offset planes)   See * Tutorial on [Iso-Planar Toolpath Generation Algorithm](http://scholarbank.nus.sg/bitstream/10635/13910/4/Chapter_3_Analysis_of_Isoplanar.pdf) * [Adaptive iso-planar tool path generation for machining of free-form surfaces](https://www.sciencedirect.com/science/article/pii/S0010448502000489), Computer-Aided Design 2003 ### Iso-scallop curves  Terminology: * **CL** = Cutter Location * **CC** = Cutter-Contact The scallop (aka cusp) height corresponds to the distance between the (ideal) design surface and the scallop curve. Making the scallop height constant corresponds to some type of uniform path that spreads as much as possible, since spreading less (i.e. overlapping more) leads to lower scallop height. By making it constant, we can avoid some types of redundant paths, which leads to some tradeoff between accuracy and time. This is not per se an optimization framework, but some * [Efficient Tool-Path Planning for Machining Free-Form Surfaces](https://manufacturingscience.asmedigitalcollection.asme.org/article.aspx?articleID=1448086), Journal of Engineering for Industry 1996 * [Constant scallop-height tool path generation for three-axis sculptured surface machining](http://www2.kuas.edu.tw/prof/hycheng/paper-3/sculptured%20surface%20machinng.pdf), Computer-Aided Design 2002 * [Iso-scallop tool path generation in 5-axis milling](https://link.springer.com/content/pdf/10.1007%2Fs00170-003-2054-7.pdf), International Journal of Advanced Manufacturing Technologies 2005 ### Energy Minimization Energy minimization methods define an energy over the surface to be processed, and then find a path by minimizing the accumulated energy while traversing the field. Related terms: * Scalar fields * Potential fields  * [Iso-level tool path planning for free-form surfaces](https://www.sciencedirect.com/science/article/pii/S0010448514000700), Computer-Aided Design 2014 * Energy minimization regarding a scalar function over surface, with two terms E=E_w+E_&kappa; * E_w enforces iso-scallop, based on the curvature of the cutter, as well as the normal curvature across the path interval * E_&kappa; enforces smoothness (so that the tool speed can be constant), based on normal and geodesic path curvature * Each term can be weighted to concentrate the optimization either towards smoother paths, or better scallop distribution (see figure)  * [Machining Potential](https://www.sciencedirect.com/science/article/pii/S0010448501001026) * [Efficiency-optimal iso-planar tool path generation for five-axis finishing machining of freeform surfaces](https://www.sciencedirect.com/science/article/pii/S0010448516301270), Computer-Aided Design 2017 * Using Direction-Based scalar fields (that describe the energy as a function of the direction) * Consider three terms: 1. The cutting strip width 2. The workpiece feedrate 3. The effective material removal rate (i.e. machine efficiency) = EMRR * Converting workpiece into triangular mesh * Using iso-planar method and optimizing the orientation, then refining tool orientation ### Genetic Algorithms * [CNC Milling Toolpath Generation Using Genetic Algorithms](http://opus.bath.ac.uk/53569/1/WesleyEssinkThesis.pdf) (PhD thesis, 2017) * [Optimization of CNC isoscallop free form surfaces machining using a genetic algorithm](https://www.sciencedirect.com/science/article/pii/S0890695505001884), International Journal of MAchine Tools and Manufacture 2006 ### Configuration-Space Search   [Optimizing tool orientations for 5-axis machining by configuration-space search method](https://www.sciencedirect.com/science/article/pii/S0010448502000775) * Separate path from orientation * Compute discretized feasible C-Space for orientations at each path position (avoiding gouging and collision) * Minimize cusp-height as objective function ### Particle Swarm Optimization (PSO)  [PSO](https://en.wikipedia.org/wiki/Particle_swarm_optimization) optimizes a problem by iteratively trying to improve a candidate solution. It does so by using a population of candidate solutions (particles), and moving these in search-space, influenced by its local best known position, and guided towards the best known position in search-space. [Improving optimization of tool path planning in 5-axis flank milling using advanced PSO algorithms](https://www.sciencedirect.com/science/article/pii/S0736584512000531) [Particle swarm optimisation (PSO)-based tool path planning for 5-axis flank milling accelerated by graphics processing unit (GPU)]()