Region-based toolpath generation for robotic milling of freeform surfaces with stiffness optimization

Because of industrial robots’ relatively low stiffness, many research efforts have been performed to improve the robot stiffness by optimizing the robot posture. For freeform surfaces with large curvature, however, the expected high stiffness posture may undergo excessive changes that exceed the robot joint speed limit. Therefore, the stiffness optimization may not achieve the expected results in actual machining owing to the limitation of robot kinematics and conventional toolpath pattern. To address this problem, a region-based toolpath generation method is proposed to improve robot stiffness in this study for robotic milling of freeform surfaces. To provide the possibility of higher stiffness robot posture, not only the redundant degree of freedom (DOF) of the robot but also the orientation of tool axis during machining is optimized. Under the influence of surface curvature and position, the change of high stiffness posture has regionality. A surface subdivision method is proposed to divide the surface into multiple sub-regions, so that actual robot posture with better stiffness can be obtained. For each sub-region, the feed direction of toolpath is optimized to further enhance robot stiffness. Simulations and experimental studies are conducted, and show that the proposed toolpath generation method can improve the robot stiffness in freeform surface machining.     

Boundary-conformed toolpath generation for trimmed free-form surfaces

In this paper, we adopt a 2D reparameterization procedure to regenerate boundary-conformed toolpaths. Three methods for the 2D reparameterization of trimmed boundaries in parametric space are examined and compared. They are the Coons method, the Laplace method, and a newly developed boundary-blending method. These three methods represent three different approaches to 2D surface parameterization, namely, the algebraic interpolation approach, the partial differential equation approach, and a geometric offsetting approach, respectively. Complete algorithms for surface reparameterization and toolpath generation are developed and implemented. The results showed that the Coons method is relatively simple yet might cause anomalies when the complexities of the boundary are high. The Laplace method is robust but takes relatively more computational time and also has the problem of uneven distribution of iso-parametrics. For the newly developed boundary-blending method, both the computational efficiency and parameterization robustness are quite good, in addition, it alleviates the uneven distribution problem appeared in the Laplace results.     

Pocketing toolpath computation using an optimization method

This paper proposes a new method of pocketing toolpath computation based on an optimization problem with constraints. Generally, the calculated toolpath has to minimize the machining time and respect a maximal effort on the tool during machining. Using this point of view, the toolpath can be considered as the result of an optimization in which the objective is to minimize the travel time and the constraints are to check the forces applied to the tool. Thus a method based on this account and using an optimization algorithm is proposed to compute toolpaths for pocket milling. After a review of pocketing toolpath computation methods, the framework of the optimization problem is defined. A modeling of the problem is then proposed and a solving method is presented. Finally, applications and experiments on machine tools are studied to illustrate the advantages of this method.     

Contour offset approach to spiral toolpath generation with constant scallop height

Recently, the application of high-speed machining (HSM) is recognized as an economically viable manufacturing technology. Even though more HSM centers have increasingly been utilized, the conventional toolpath generation methods are usually employed in practice. But the conventional methods have inherent limitations for the HSM application.This paper presents a new toolpath generation algorithm for high-speed finish cutting process. In order to minimize the fluctuation of cutting load and the possibility of chipping on the cutting edge in HSM, a spiral topology toolpath that is to cut continuously with the minimum number of cutter retractions during the cutting operations is developed. This algorithm begins with the contour offset procedure along the boundary curve of the sculptured surface being machined. In the offset procedure, the offset distance is determined such that the scallop height maintains a constant roughness to ensure higher levels of efficiency and quality in high-speed finish machining. Then, the spiral path is generated as a kind of the diagonal curve between the offset curves. This path strategy is able to connect to a neighbor path without a cutter retraction. Therefore, the minimum tool retraction toolpath can be generated. And, it allows the sculptured surface incorporating both steeper and flatter areas to be high-speed machined. Based on these techniques, experimental results are given to verify the proposed approach.     

Intelligent toolpath selection via multi-criteria optimization in complex sculptured surface milling

A new approach is presented the first time in the literature to generate multi-criteria optimized toolpaths for the complex sculptured surface machining. This is achieved by developing a mathematical solution that consists of the physical relationship between the mean resultant forces, cycle times and scallop heights. These three critical process outputs in machining are conflicting with each other. In other words, there are tradeoffs between cutting force magnitudes, cycle time and scallop height. This triple bounded problem in machining is solved in this article by using the objective weighting based algorithm. The multi-criteria toolpath optimization method introduced here for sculptured surface machining increases the controllability of the process with the specified criteria. The method also allows determining all pareto optimal solutions and all possible weights of each criteria. Moreover, the method eases to observe and analyze the trade-off between each criterion, facilitate the limitation and minimization of each criterion and determine corresponding toolpath for each solution. This solution produces optimized toolpaths according to preset constraints for mean cutting force, cycle time and scallop height. The method is a generalized solution for determining optimized toolpaths based on given constrains in free-form surface machining. In order to validate the multi-criteria toolpath optimization method, experiments at various conditions are performed on free-form machining and an example is presented in this article.     

Toolpath Interpolation and Smoothing for Computer Numerical Control Machining of Freeform Surfaces: A Review

Driven by the ever increasing demand in function integration, more and more next generation high value-added products, such as head-up displays, solar concentrators and intra-ocular-lens, etc., are designed to possess freeform (i.e., non-rotational symmetric) surfaces. The toolpath, composed of high density of short linear and circular segments, is generally used in computer numerical control (CNC) systems to machine those products. However, the discontinuity between toolpath segments leads to high-frequency fluctuation of feedrate and acceleration, which will decrease the machining efficiency and product surface finish. Driven by the ever-increasing need for high-speed high-precision machining of those products, many novel toolpath interpolation and smoothing approaches have been proposed in both academia and industry, aiming to alleviate the issues caused by the conventional toolpath representation and interpolation methods. This paper provides a comprehensive review of the state-of-the-art toolpath interpolation and smoothing approaches with systematic classifications. The advantages and disadvantages of these approaches are discussed. Possible future research directions are also offered.

     

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.     

基于波前法的参数曲面有限元网格生成算法

为克服参数曲面有限元网格生成中的单元形状映射畸变问题,提出一种曲面有限元网格自动生成算法.该算法由弹性矢量确定曲面上新节点的生成方向和空间位置,利用相应的参数域网格进行新单元拓扑相容性判断.在生成闭曲面网格时,通过添加参/虚边界棱边对闭曲面边界进行调整,确保闭曲面边界信息相对其参数域的完整性;在给出闭曲面极点初始化方法和适当设置单元边线段相等条件的基础上,该算法适用于各种不同形式闭曲面的网格自动生成.实验算例表明,文中算法可生成质量良好的参数曲面和组合面有限元网格.     

多裁剪自由曲面生成有限元网格的实现

论述了多裁剪自由曲面生成有限元曲面网格的几个关键技术.采用了推进波前法生成曲面网格,给出了核心算法;在曲面算法中运用了介于参数法与直接法之间的新方法.针对求解曲面上最优点的参数域反算问题,引入了切矢逆求方法,可使迭代次数大为降低.测试表明,该算法快速、稳定.对大型的多裁剪自由曲面生成的曲面有限元网格,可直接用于有限元计算.     

Automatic generation of gouge-free and angular-velocity-compliant five-axis toolpath

Existing works in automatic generation of interference-free five-axis surface machining toolpaths bear a serious drawback — in order to avoid the obstacles, the tool is often required to make drastic change in its orientation between neighboring contact points. Such a quick change in the tool’s orientation can never be made possible in reality due to the stringent physical limit on the speed and acceleration of the rotary motions of the machine tool. The usual ad hoc solution to this problem is to smooth the toolpath in the configuration space, which, however, is prone to special situations of failure and is not able to guarantee the absolute compliance with the given angular velocity limit. In this paper we present an approach to this problem by directly involving the angular velocity limit in the search process. The presented algorithm will automatically generate a five-axis toolpath that not only is interference-free but also guarantees the angular-velocity compliance. Delicate computation and manipulation of visibility maps and their derivative data ensure that the proposed algorithm is computationally feasible with acceptable computing time and memory requirement. Test examples are given to demonstrate the promising use of the proposed solution.     

SHELL ADAPTIVE TRIANGULATION OF TRIMMED NURBS SURFACE

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Isophote interpolation

The isophote is an important class of characteristic curves on a parametric surface. Accordingly, as a kind of feature based path generation method, isophote based tool paths has been proposed as an important path pattern for parametric surface machining. In this paper, an approach has been proposed for the isophote interpolation on a parametric surface. The paper has related the arc-length derivatives to time derivatives of parameters along the isophote. The results are then used to derive the parametric interpolation. The isophote curve interpolation is developed based on parametric interpolation. The proposed interpolation guarantees that interpolated points always stay on the parametric surface. An improvement interpolation has been presented to alleviate inclination errors and point deviation from the isophote. Simulations of isophote interpolation have been carried out to verify the effectiveness of the proposed algorithm. The proposed algorithm has applications in real time tool path interpolation for the machining of parametric surfaces.     

IMS10-image-based milling toolpaths with tool engagement control for complex geometry

This paper presents a NC toolpath generation strategy with tool engagement control for arbitrarily complex discrete part geometry, which reduces machining time and tool wear and can be used in high speed machining. The toolpath computation is based on image models for design part, raw stock and cutting tool, and involves pixel-based simulation of the milling process. Simulation results and comparison with existing methods are presented.     

汽车覆盖件模具凹,凸模数控加工数据转换技术的开发及应用

本文论述了与数控加工数据转换技术有关的曲线、曲面、等距曲面、曲面求交和曲面修剪的算法。重点对有理Ｂ样条曲线曲面的方法及特点进行了探讨。同时，还讨论了如何合理地生成拟合曲面的方法及刀具运行轨迹的生成和编辑方法。最后介绍了该技术在汽车覆盖件模具制造上的应用。     

An algorithm for the interpolation of hybrid curves

Real time tool path generation consists of off-line design and real time interpolation of tool paths. An hybrid curve is the intersection of a parametric surface and an implicit surface. Previous work in tool path interpolation focused mainly in the interpolation of parametric curves. Tool paths designed by drive surface methods are hybrid curves which, in general, cannot be represented as parametric curves. An algorithm for the interpolation of hybrid curves is proposed in this paper. The algorithm is based on interpolation of the projection of the hybrid curve into the parametric domain. Each increment involves a second-order interpolation step augmented by iterative error reduction.Simulations of hybrid curve interpolation have been carried out. They are based on practical surfaces represented as NURB surfaces and implicit surfaces including a plane, a cylinder and a high order algebraic surface. They demonstrate that under typical machining conditions, interpolation error is well within the accuracy requirements of typical machining and that the use of one iteration error reduction can significantly reduce the path deviation. These show that the proposed algorithm is potentially useful for tool path interpolation for the machining of parametric surfaces.     

Approximate development of trimmed patches for surface tessellation

This paper presents a method for constructing an auxiliary planar domain of triangulation for tessellating trimmed parametric surface patches. By minimizing a mapping error function, an approximate locally isometric mapping between a given trimmed parametric surface patch and its triangulation domain is constructed. In this way the shape of triangular elements on the triangulation domain is approximately preserved when mapped into three-dimensional space. We also provide an efficient method to achieve a good initial guess for the minimization of the mapping error function. Furthermore, our proposed method guarantees a homeomorphism between a triangulation domain and parametric space/given surface patch by robustly removing the possibility of self-intersection on the developed surface net. Practical application of the proposed algorithm can include the formation of ship hulls, ducts, shoes, clothing and automobile parts as well as the surface meshing procedure.     

Toolpath planning algorithm for the ablation process using energy sources

Ablation processes using various energy sources such as lasers, electrical power and ultrasonic sources have been widely used in industry to ablate workpieces made of hard-to-cut and temperature resistive materials. Even though the cutting mechanism of the ablation process is different from that of the mechanical cutting process, an identical toolpath of the mechanical cutting process has been applied to the ablation process. An inappropriate toolpath for the ablation process may result in a lower dimensional accuracy of the ablated part. Therefore, a new toolpath planning algorithm considering the characteristics of the energy source is required. In this paper, a toolpath planning algorithm for the ablation process is proposed. The proposed algorithm consists of three steps: (1) The generation of a valid toolpath element, (2) the storage of toolpath elements and the creation of sub-groups, (3) the linking of sub-groups. New guidelines on the toolpath demanded by the ablation process are studied. A new idea involving the use of a storage matrix is applied to the storage of toolpath elements and the creation of sub-groups. In order to verify the applicability of the proposed algorithm, the proposed toolpath planning algorithm has been implemented and tested with practical examples.     

裁剪面的一类参数变换

给出了一类可以保持几何与拓扑信息一致性的裁剪面的参数变换定理及其算法。首先,确定了参数变换对裁剪面表示信息的影响。然后,根据参数变换后几何与拓扑信息的一致性要求,给出了对裁剪面表示信息进行调整的方法。最后,通过建立参数变换的关系,以裁剪球面为例阐述了这类参数变换的具体实现方法。     

Process planning strategies for solid freeform fabrication of metal parts

Process planning of additive manufacturing of metals is a research interest because of the applications of solid freeform fabrication of metal parts in industry. The strategy is to transform the model of the part into the combinations of 2D layers that will be deposited using different fabrication methods. Process planning for metal deposition in this paper consists of three major modules: spatial decomposition, slicing of the part, and toolpath generation for every slicing layer. Algorithmic improvements are proposed and implemented for these major modules. For spatial decomposition, 3D part decomposition based on modular boundary models and centroidal axis extraction methods are combined to decompose parts more robustly and reliably. For generating slicing layers, a planning process for building non-uniform layers is investigated to greatly increase the variety of the parts that can be manufactured without the need of support structure. For toolpath generation methods, optimization of the generated toolpath is studied especially for complex thin-wall structures to ensure the deposition quality. Experiments were carried out to evaluate the improvements of the major modules of process planning strategies for rapid manufacturing.     

Local asymmetrical corner trajectory smoothing with bidirectional planning and adjusting algorithm for CNC machining

The linear motion command (G01) is a widely used command format in CNC machining. However, the tangential direction discontinuity at the corner junction will cause velocity fluctuations and excite the structural vibration of machine tools. Corner smoothing methods with controlled tolerance are used to obtain continuous smooth motion. Typically, most methods generate a symmetrical cornering trajectory around the angle bisector, and the trajectory generally decelerates first and then accelerates, which limits the velocity increase. In this paper, a novel local asymmetrical corner trajectory smoothing method is proposed, which can realize accelerated/decelerated cornering transition. The proposed method can obtain the analytical solution in one step, which is different from two-step geometric-based corner path smoothing, and can generate the same cornering trajectory in back-and-forth parallel toolpath. In addition, this paper proposes a bidirectional planning and adjusting algorithm for the situation where smoothed cornering paths are close to each other or even overlap. The algorithm can generate a jerk-limited trajectory by coordinating the cornering error of adjacent corners, while respecting the user-specified tolerance. Experimental results demonstrate the effectiveness of the proposed method in contour accuracy and cycle time for CNC machining along short-segmented toolpath.