Modeling of cutting geometry and forces for 5-axis sculptured surface machining

5-Axis sculptured surface machining is simulated using discrete geometric models of the tool and workpiece to determine the tool contact area, and a discrete mechanistic model to estimate the cutting forces. An extended Z-buffer model represents the workpiece, while a discrete axial slice model represents the cutting tool. Determination of the contact area for a given tool move requires a swept envelope (SWE) of the tool path. The SWE is used to find the intersections of the tool envelope with Z-buffer elements (ZDVs) representing the workpiece. A 3-axis approximation of the 5-axis tool movement is used to simplify the calculations while maintaining a desired level of accuracy. The intersection of the SWE with each ZDV yields segments which are used to find the contact area between the cutter and the workpiece for a given tool path. The contact area is subsequently used with the discrete force model to calculate the vector cutting force acting on the tool.     

计算机数控加工仿真中误差检测技术的研究与实现

为了在数控加工仿真系统中对对数控加工代码的正确性进行分析和评定，本文提出一种简单快速的误差检测算法，该算法的基本思想是，在对零件模型进行Z空间离散的基础上，通过对离散模型分别与零件曲面的STL集合及刀位切削段的拉掠面进行求交运算，从而获得零件设计曲面和加工结果曲面的几何表示，法向投影误差计算法精确，简单地计算出零件加工误差的分布。     

Hybrid cutting simulation via discrete vector model

Geometric cutting simulation and verification play an important role in detecting NC machining errors in mold and die manufacturing, thereby reducing the correcting time and cost on the shop floor. According to workpiece model, current researches may be categorized into view-based, solid-based, and discrete vector-based methods. Each methodology has its own strengths and weaknesses in terms of computing speed, representation accuracy, and its ability to perform numerical inspection. This paper proposes a cutting simulation methodology via a hybrid workpiece model which consists of the general discrete vector model and its simplified model. Workpiece modeling scheme, cutting simulation via tool swept surface modeling and vector intersection, and some case studies of mold and die machining are presented in this paper.     

Computing of the actual shape of removed material for five-axis flat-end milling

This paper describes an algorithm that predicts the shape of material removed by a flat-end milling tool, and this may be used to compute machining strip width and scallop height at different positions of the tool path track. The algorithm computes swept sections, profiles which are swept by a moving tool bottom by passing through given planes. The technique is applicable for finish and semi-finish multi-axis milling strategies that use flat-end tools. For these strategies, the algorithm complexity can be reduced from computation of the 3D envelope of swept volumes to computation of plane-circle intersections. A new adaptive derivative-free method to sample tool motion provides robust means to generate intermediate tool positions. The step length is constrained by and dependent on different geometrical measures. At each point of a tool path, in the plane perpendicular to the cutting direction, the bottom profile of the swept section is an estimate of the profile of material left. By calculating the distance between part geometry and the computed profile of removed material, machining strip width and a scallop profile can be derived. These results can be used by tool path generation and validation routines to accurately determine the step-over between tool path tracks and surface quality.     

Accurate tool position for five-axis ruled surface machining by swept envelope approach

This paper presents a swept envelope approach to determining tool position for five-axis ruled surface machining. The initial tool position is traditionally located to contact with two directrices of a ruled surface. The swept profile of the tool is then determined based on the tool motion. By comparing the swept profile with the ruled surface, the tool position is corrected to avoid machining errors. The cutter's swept envelope is further constructed by integrating the intermediate swept profiles, and applied to NC simulation and verification. This paper presents the explicit solution for the swept profile of a taper-end cutter in five-axis ruled surface machining. The relation of the ruled surface geometry, the tool motion and the machining errors is developed. Therefore, the error sources can be detected early and prevented during tool path planning. The explicit swept envelope indicates that the machined surface is not a ruled surface in five-axis ruled surface machining. Manufacturing industries should take extra care in high precision ruled surface machining. Computer illustrations and example demonstrations are shown in this paper. The results reveal that the developed method can accurately position tool location and reduce machining errors for five-axis ruled surface machining.     

CPU–GPU Parallel Framework for Real‐Time Interactive Cutting of Adaptive Octree‐Based Deformable Objects

A software framework taking advantage of parallel processing capabilities of CPUs and GPUs is designed for the real‐time interactive cutting simulation of deformable objects. Deformable objects are modelled as voxels connected by links. The voxels are embedded in an octree mesh used for deformation. Cutting is performed by disconnecting links swept by the cutting tool and then adaptively refining octree elements near the cutting tool trajectory. A surface mesh used for visual display is reconstructed from disconnected links using the dual contour method. Spatial hashing of the octree mesh and topology‐aware interpolation of distance field are used for collision. Our framework uses a novel GPU implementation for inter‐object collision and object self collision, while tool‐object collision, cutting and deformation are assigned to CPU, using multiple threads whenever possible. A novel method that splits cutting operations into four independent tasks running in parallel is designed. Our framework also performs data transfers between CPU and GPU simultaneously with other tasks to reduce their impact on performances. Simulation tests show that when compared to three‐threaded CPU implementations, our GPU accelerated collision is 53–160% faster; and the overall simulation frame rate is 47–98% faster.     

Global stability predictions for flexible workpiece milling using time domain simulation

This paper describes the use of peak-to-peak (PTP) force diagrams for machining stability prediction and validates its suitability for milling processes where the workpiece is considerably more flexible than the machine-tool system. These diagrams result from numerous executions of a time domain simulation which includes both the tool and workpiece dynamics and a mechanistic force model. The applicability of the PTP force diagram is validated experimentally through peripheral milling tests of thin-walled structures. Measured and simulated cutting forces are compared. It is shown that the PTP diagrams offer the global stability information which is provided by the traditional lobe diagram, while preserving the detailed, local information provided by time domain simulation.     

Precise algebraic-based swept volumes for arbitrary free-form shaped tools towards multi-axis CNC machining verification

This paper presents an algebraic based approach and a computational framework for the simulation of multi-axis CNC machining of general freeform tools. The boundary of the swept volume of the tool is precisely modeled by a system of algebraic constraints, using B-spline basis functions. Subdivision-based solvers are then employed to solve these equations, resulting in a topologically guaranteed construction of the swept volume. The presented algebraic-based method readily generalizes to accept tools of arbitrary free-form shape as input, and at the same time, delivers high degree of precision.Being a common representation in CNC simulations, the computed swept volume can be reduced to a dexels’ representation. Several multi-axis test cases are exhibited using an implementation of our algorithm, demonstrating the robustness and efficacy of our approach.     

High accuracy NC milling simulation using composite adaptively sampled distance fields

We describe a new approach to shape representation called a composite adaptively sampled distance field (composite ADF) and describe its application to NC milling simulation. In a composite ADF each shape is represented by an analytic or procedural signed Euclidean distance field and the milled workpiece is given as the Boolean difference between distance fields representing the original workpiece volume and distance fields representing the volumes of the milling tool swept along the prescribed milling path. The computation of distance field of the swept volume of a milling tool is handled by an inverted trajectory approach where the problem is solved in tool coordinate frame instead of a world coordinate frame. An octree bounding volume hierarchy is used to sample the distance functions and provides spatial localization of geometric operations thereby dramatically increasing the speed of the system. The new method enables very fast simulation, especially of free-form surfaces, with accuracy better than 1 micron, and low memory requirements. We describe an implementation of 3 and 5-axis milling simulation.     

数控仿真技术的回顾与评述

本文在对当前国内外数控切削加工几何仿真和切削过程力学仿真的两个并行发展的研究领域的研究现状和成果的分析评述的基础上，指出了仿真的发展趋势，并提出一种几何仿真和力学仿真相结合的更精确的试切模型。     

Tool path generation for multi-axis freeform surface finishing with the LKH TSP solver

In freeform surface finishing, there are three major types of tool path topologies: the direction-parallel type, the contour–parallel type and the space-filling curve (SFC) type. The SFC topology is capable of covering the whole surface with only one path. In this paper, we present a new way of planning the SFC type tool path by formulating the planning task as a traveling salesman problem (TSP). The optimal path is generated in two steps. Firstly, a set of regular cutter contact (CC) points is generated on the input surface. A cutting simulation method is developed to evaluate the scallop error and determine the position of the next CC point in cross-feed direction. This method is free of local surface curvature assumptions and is therefore accurate for big cutters. Secondly, the obtained CC points are input into an efficient TSP solver LHK for the optimal CC point linking sequences. To stop the CC points from diagonal linking or penetrating linking, the Euclidean distance evaluation function for two CC points is redefined in LHK. The proposed tool path generation method is verified with several freeform surface examples; the results show that the method can automatically find the optimal feed direction and it can generate shorter tool path than the traditional SFC method. The feasibility of the proposed method is also verified by a cutting experiment.     

Simultaneous optimization of tool path and shape for five-axis flank milling

By representing the swept envelope of a generic rotary cutter as a sphere-swept surface, our previous work on distance function based tool path optimization is extended to develop the model and algorithm for simultaneous optimization of the tool path and shape for five-axis flank milling. If the tool path is fixed, a novel tool shape optimization method is obtained. If the tool shape is fixed, a tool path optimization method applicable to any rotary cutter is obtained. The approach applies to non-ruled surfaces, and also finds applications in cutter dimension optimization and flank millable surface design. Numerical examples are given to confirm its validity.     

Modelling and simulation of whirling process based on equivalent cutting volume

The thread whirling is an efficient and precise machining process for manufacturing of screws. The shaping motion of whirling is complex and difficult to model. In this paper, a novel model basing on equivalent cutting volume is proposed. The cutting force and the chip morphology are investigated to validate the model. The simulation of cutting force is in good agreement with the experimental results with error less than 16.5%. A chip with saw-toothed edges is obtained from simulation and for experimental verification. A case study on the effect of the tool edge geometry on cutting forces is also presented. The simulation results show that the tool edge geometry greatly influences the cutting forces. The tool with round edge is a good choice for reducing the cutting forces. The ratio of a_c/R_e holds the balance in selecting the parameter of cutting conditions. The model is applicable for the simulation of whirling process and can be used for parameter optimisation of the cutting tool edge.     

Prediction of cutting forces in 3-axes milling of sculptured surfaces directly from CAM tool path

In the present work a new approach for the modelling of milling is described. The cutting forces are calculated for milling operations directly from the tool path provided by a Computer Assisted Manufacturing program. The main idea consists in using tool position points coming from CAM data in order to calculate the local inclination angle of the generated surface and then the tool engagement in the machined material. A good approximation for global and local cutting forces can be obtained when an analytical model able to predict the cutting forces for 3-axes milling is used. Two approaches are proposed to calculate the local cutting forces to show the versatility of the method. The first method uses a thermomechanical approach using a Johnson & Cook constitutive law while the second is based on classical cutting coefficients. Some results are presented for wavelike form and free form machining tests and are compared with experimental data obtained in roughing and finishing of 42CrMo4 steel. Results are satisfactory and the capability of the method to predict the resultant surface roughness is shown.     

Optimal and collision free tool posture in five-axis machining through the tight integration of tool path generation and machine simulation

The generation of collision free NC-programs for multi-axis milling operations is a critical task, which leads to multi-axis milling machines being exploited below their full capacities. Today, CAM systems, generating the tool path, do not take the multi-axis machine movements into account. They generate a multi-axis tool path, described by a sequence of tool postures (tool tip+tool orientation), which is then converted by a NC-postprocessor to a machine specific NC-program. As the postprocessing is normally done in batch mode, the NC-programmer does not know how the machine will move and the chance for having collisions between (moving) machine components is often very high. The execution of a machine test run or the application of a machine simulation system (NC-simulation) is the only solution to inform the NC-programmer about possible machine collisions during operation.This paper describes a multi-axis tool path generation algorithm where the tool orientation is optimised to avoid machine collisions and at the same time to maximise the material removal rate along the tool track. To perform efficient collision avoidance, the tool path generation module (traditional CAM), the postprocessing (axes transformation) and machine simulation has been integrated into one system. Cutting tests have been carried out to define the allowable tool orientation changes for optimisation and collision avoidance without disturbing the surface quality.The developed multi-axis tool path generation algorithm is applicable for the machining of several part surfaces within one operation. This, together with tool path generation functionality to adapt the tool orientation for both, maximal material removal and avoidance of collisions between (moving) machine components, are the innovative aspects of the presented research work.     

基于声线跟踪法开发超声无损检测动态仿真软件

以“声线跟踪法”为基础，运用面向对象的编程语言VisualC＋＋和三维场景开发工具OpenGL，按照面向对象的程序设计思想开发了超声波无损检测仿真软件。该系统实现了超声检测过程的三维可视化并对超声波传播路径和A型显示进行了较为准确的模拟。该文对仿真过程中的三维介质建模和传播路径模拟计算等关键问题进行了详细的讨论，采用CSG／B-Rep混合模型表示法对三维介质模型进行快速建模，并且采用声线跟踪法对传播路径进行较为准确的模拟。最后通过仿真实例，验证了算法的有效性。     

Process planning for Floor machining of 2½D pockets based on a morphed spiral tool path pattern

This work proposes a process planning for machining of a Floor which is the most prominent elemental machining feature in a 2½D pocket. Traditionally, the process planning of 2½D pocket machining is posed as stand-alone problem involving either tool selection, tool path generation or machining parameter selection, resulting in sub-optimal plans. For this reason, the tool path generation and feed selection is proposed to be integrated with an objective of minimizing machining time under realistic cutting force constraints for given pocket geometry and cutting tool. A morphed spiral tool path consisting of G¹ continuous biarc and arc spline is proposed as a possible tool path generation strategy with the capability of handling islands in pocket geometry. Proposed tool path enables a constant feed rate and consistent cutting force during machining in typical commercial CNC machine tool. The constant feed selection is based on the tool path and cutting tool geometries as well as dynamic characteristics of mechanical structure of the machine tool to ensure optimal machining performance. The proposed tool path strategy is compared with those generated by commercial CAM software. The calculated tool path length and measured dry machining time show considerable advantage of the proposed tool path. For optimal machining parameter selection, the feed per tooth is iteratively optimized with a pre-calibrated cutting force model, under a cutting force constraint to avoid tool rupture. The optimization result shows around 32% and 40% potential improvement in productivity with one and two feed rate strategies respectively.     

数控加工仿真系统的研究与应用

介绍数控加工仿真系统的整体设计,提出格栅voxel三维实体建模方法,刀具扫描体的生成算法,实现了刀具切削工件过程的动态仿真,并对碰撞检查算法进行了初步的研究.基于以上方法,建立了蓝天数控系统的加工仿真系统,在加工前对加工程序进行验证,在加工时对刀具轨迹的执行、工件的切削过程等进行实时监控.     

Process planning for Floor machining of 2½D pockets based on a morphed spiral tool path pattern

This work proposes a process planning for machining of a Floor which is the most prominent elemental machining feature in a 2½D pocket. Traditionally, the process planning of 2½D pocket machining is posed as stand-alone problem involving either tool selection, tool path generation or machining parameter selection, resulting in sub-optimal plans. For this reason, the tool path generation and feed selection is proposed to be integrated with an objective of minimizing machining time under realistic cutting force constraints for given pocket geometry and cutting tool. A morphed spiral tool path consisting of G¹ continuous biarc and arc spline is proposed as a possible tool path generation strategy with the capability of handling islands in pocket geometry. Proposed tool path enables a constant feed rate and consistent cutting force during machining in typical commercial CNC machine tool. The constant feed selection is based on the tool path and cutting tool geometries as well as dynamic characteristics of mechanical structure of the machine tool to ensure optimal machining performance. The proposed tool path strategy is compared with those generated by commercial CAM software. The calculated tool path length and measured dry machining time show considerable advantage of the proposed tool path. For optimal machining parameter selection, the feed per tooth is iteratively optimized with a pre-calibrated cutting force model, under a cutting force constraint to avoid tool rupture. The optimization result shows around 32% and 40% potential improvement in productivity with one and two feed rate strategies respectively.     

Iso-planar piecewise linear NC tool path generation from discrete measured data points

This article presents a method of generating iso-planar piecewise linear NC tool paths for three-axis surface machining using ball-end milling directly from discrete measured data points. Unlike the existing tool path generation methods for discrete points, both the machining error and the machined surface finish are explicitly considered and evaluated in the present work. The primary direction of the generated iso-planar tool paths is derived from the projected boundary of the discrete points. A projected cutter location net (CL-net) is then created, which groups the data points according to the intended machining error and surface finish requirements. The machining error of an individual data point is evaluated within its bounding CL-net cell from the adjacent tool swept surfaces of the ball-end mill. The positions of the CL-net nodes can thus be optimized and established sequentially by minimizing the machining error of each CL-net cell. Since the linear edges of adjacent CL-net cells are in general not perfectly aligned, weighted averages of the associated CL-net nodes are employed as the CL points for machining. As a final step, the redundant segments on the CL paths are trimmed to reduce machining time. The validity of the tool path generation method has been examined by using both simulated and experimentally measured data points.