A Review of Vector Field-Based Tool Path Planning for CNC Machining of Complex Surfaces
Abstract
1. Introduction
2. Conventional Tool Path Planning Methods for Complex Surfaces
- (1)
- The isoparametric line method, first proposed by Loney et al. [18], is widely used in multi-coordinate machining due to its simplicity, as it generates paths along surface parametric lines [19]. However, its critical limitation lies in the non-linear mapping between parameter space and Euclidean space, leading to uneven path spacing and potential undercutting; this makes it unsuitable for highly curved surfaces. He et al. [20] addressed this by developing an adaptive mesh optimization method, which reduces transformation deviation but increases computational complexity, highlighting a trade-off between accuracy and efficiency that subsequent methods (e.g., the truncated plane method) sought to resolve.
- (2)
- The intercept plane method generates paths via intersections between parallel planes and the machined surface [21], showing strong applicability to sheared parametric surfaces. However, its reliance on solving nonlinear equations leads to high computational costs, and conservative line spacing (to ensure accuracy) reduces efficiency; this contrasts the isoparametric line method, which is simpler but less adaptable, revealing a fundamental tension between universality and computational feasibility in traditional path planning.
- (3)
- The equal illuminance line method was first proposed in 1984. There are many points on a surface with the same illuminance, and the curve formed by connecting these points is called the line of equal illuminance. Since the illuminance side reflects the smoothness of a surface, the method was initially used to check the continuity of surfaces. Later, Han et al. [22] proposed the following innovative idea: the complex surface of a workpiece surface is approximated as consisting of multiple piecewise straight curves. Under this assumption, we further connect points with the same illumination level to each other to form a series of boundary curves or localization buses located on the surface. More accurate positioning is achieved, so the method is also used in five-axis CNC machining with more and more accurate positioning coordinates.
- (4)
- The basic idea of the mapping method is to first map the three-dimensional surface to be machined into a two-dimensional plane, then calculate the tool trajectory for the two-dimensional plane. Following this, the tool position points of the obtained two-dimensional plane are corresponded to the three-dimensional surface one by one through the mapping to obtain the tool trajectory [23]. Han et al. [24] applied this method to complex impeller surfaces by mapping the trajectories from the parametric domain to the physical domain to obtain the tool path. For the mapping method, the direction of 3D parametric mapping directly affects the geometric fidelity and kinematic characteristics of the tool trajectory, which in turn determines the machining efficiency and molding accuracy of the method. Therefore, this method is widely used in tool path planning for curved cavity-like structures and multi-feature combination surfaces.
- (5)
- The equal residual height method is designed to improve machining efficiency, reduce machining time, and ensure machining accuracy by maintaining the machining residual height between adjacent tool paths within a preset maximum allowable value [25]. This method was first proposed by Suresh et al. [26] and is currently the most widely used method.
3. Vector Field-Based Tool Path Planning Methods for Complex Surfaces
3.1. Vector Field-Based Tool Attitude Optimization
3.2. Vector Field-Based Tool Position Optimization
- (1)
- Maximum machining bandwidth [49]. In tool path planning, it is determined that the tool can move with the maximum machining bandwidth by considering the vectorial characteristics of the tool path (e.g, direction, speed, etc.) and the geometry of the machining area. However, it has high computational complexity and high equipment requirements, and it is more dependent on machining experience.
- (2)
- Optimized kinematic performance [50]. In the field of CNC machining, the kinematic characteristics of each feed axis of the machine tool are optimized by optimizing the direction and variation of the tool path and the tool axis vector field, thus ensuring speed smoothing, machining stability, and load balancing of the machine tool during the machining process.
- (3)
- Minimum energy consumption [51]. Under the premise of meeting the requirements of the machining task, the reasonable adjustment of the tool axis vector field to optimize the trajectory of the tool, so that the tool in the execution of the machining task requires a minimum of energy, thus reducing the production cost.
- (4)
- Maximum material removal rate [52]. This refers to the planning of the tool’s trajectory to achieve the optimization of the tool’s path, speed, acceleration, and other parameters through the planning of the tool axis vector field, so as to maximize the volume of material removed from the machined part per unit of time.
- (5)
- Optimal smoothness [53]. When performing CNC machining, the vector field is used to optimize the feed direction of the tool so that the machined surface achieves the optimum smoothness. This method not only reduces the roughness of the machined surface and improves the machining quality, but also reduces the tool wear and lowers the machining cost.
- (6)
- Area subdivision [54]. Area subdivision machining usually refers to the CNC machining of complex geometries. Based on the vector field, the entire machining area is subdivided into multiple sub-areas, and different machining strategies and parameter settings are formulated for the characteristics and needs of each sub-area to optimize the machining process and improve the quality of the product. In conclusion, area subdivision machining is an effective machining optimization method, which can improve production efficiency, reduce cost, improve product quality, adapt to market demand, and improve production safety.
3.2.1. Tool Position Optimization Based on Maximum Machining Bandwidth
3.2.2. Tool Position Optimization Based on Best Kinematic Performance
3.2.3. Tool Position Optimization Based on Minimum Energy Consumption
3.2.4. Tool Position Optimization Based on Maximum Material Removal
3.2.5. Smoothness-Based Optimal Tool Position Optimization
3.2.6. Tool Position Optimization Based on Area Segmentation
4. Conclusions and Outlook
- (1)
- The traditional tool path planning methods are still confined to the point-by-point trajectory design at the purely geometric level, and the layout form depends on the selection of the initial path. Additionally, there are fewer methods to consider the tool trajectory at the integrated level of geometry, kinematics, and dynamics, which are not able to take into account the physical characteristics of the surface geometry and have difficulty realizing the overall control of the tool trajectory. Therefore, it is necessary to consider from the perspective of geometry, kinematics, and dynamics.
- (2)
- Regarding the optimization of tool posture based on vector field, the current research mainly focuses on the smoothness of the feed vector; however, the consideration factors are too single. Therefore, the multimodal vector field data, such as the CAD model, feed speed curve, spindle torsion angle, vibration spectrum, etc., should be integrated to establish cross-modal correlation through models similar to the Contrastive Language–Image Pretraining model (CLIP-like model), to realize the comprehensive optimization of tool attitude.
- (3)
- In the optimization of tool position based on vector field, the current is mainly based on vector field from the machining bandwidth, the best motion performance, the minimum energy consumption, the maximum material removal rate, the maximum feed rate, and so on, as the goal to achieve the optimization of the tool path. However, the above optimization objectives are mainly for the optimization of the target offline value. In the future, with the development of artificial intelligence, digital twin, image processing technologies [81,82], and wireless sensing technology, based on the sensor feedback real-time correction vector field, dynamic adjustment of the tool position, our goal is to achieve the machining process of “perception—decision-making—execution” of the closed-loop optimization, and then realize the intelligent, real-time, multi-objective optimization of complex surfaces of high-precision machining.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Method Category | Specific Methods | Advantages | Disadvantages | Applicability |
---|---|---|---|---|
Conventional Tool Path Planning | Isoparametric Line Method | Simple and practical; widely used in multi-coordinate CNC machining. | Deviation between parameter space and Euclidean space; potential undercutting. | Parametric surfaces with relatively regular mesh structures. |
Truncated Plane Method | Good applicability; suitable for sheared parametric surfaces. | Complex calculations (solving nonlinear equations); long tool path due to conservative line spacing. | General complex surfaces; widely used in CAD/CAM systems. | |
Iso-Illumination Line Method | Accurate positioning; applicable to five-axis CNC machining. | Initially designed for surface continuity checking; limited in complex geometries. | Surfaces requiring high positioning accuracy. | |
Mapping Method | Transforms 3D problems to 2D for easier calculation. | Mapping quality affects trajectory accuracy; challenging for highly complex surfaces. | Curved cavity-like structures and multi-feature combination surfaces. | |
Equal Residual Height Method | Guarantees both machining efficiency and accuracy. | Large calculation volume; lower efficiency in the early stage (alleviated by modern computing). | Parametric surfaces and mesh surface models with high-precision requirements. | |
Vector Field-Based Tool Path Planning | Tool Attitude Optimization | Improves machining smoothness and kinematic performance; reduces tool vibration. | Some methods ignore machine tool rotary axis performance; may cause servo tracking errors. | Scenarios requiring high smoothness, such as high-speed milling. |
Tool Position Optimization (Maximum Bandwidth) | Enhances machining efficiency by maximizing cutting width. | High computational complexity; dependent on machining experience and equipment. | Large or structurally complex parts. | |
Tool Position Optimization (Kinematic Performance) | Ensures speed smoothness, stability, and load balancing. | Requires comprehensive consideration of multi-axis constraints; complex parameter tuning. | High-speed and high-precision machining processes. | |
Tool Position Optimization (Minimum Energy Consumption) | Reduces production cost by minimizing energy usage. | Limited by machining task requirements; needs balance with accuracy. | Energy-sensitive manufacturing environments. |
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Xie, S.; Liu, Z. A Review of Vector Field-Based Tool Path Planning for CNC Machining of Complex Surfaces. Symmetry 2025, 17, 1300. https://doi.org/10.3390/sym17081300
Xie S, Liu Z. A Review of Vector Field-Based Tool Path Planning for CNC Machining of Complex Surfaces. Symmetry. 2025; 17(8):1300. https://doi.org/10.3390/sym17081300
Chicago/Turabian StyleXie, Shengchang, and Zhiping Liu. 2025. "A Review of Vector Field-Based Tool Path Planning for CNC Machining of Complex Surfaces" Symmetry 17, no. 8: 1300. https://doi.org/10.3390/sym17081300
APA StyleXie, S., & Liu, Z. (2025). A Review of Vector Field-Based Tool Path Planning for CNC Machining of Complex Surfaces. Symmetry, 17(8), 1300. https://doi.org/10.3390/sym17081300