5-axis Flank Research Articles

On C0 and C1 continuity of envelopes of rotational solids and its application to 5-axis CNC machining

We study the smoothness of envelopes generated by motions of rotational rigid bodies in the context of 5-axis Computer Numerically Controlled (CNC) machining. A moving cutting tool, conceptualized as a rotational solid, forms a surface, called envelope, that delimits a part of 3D space where the tool engages the material block. The smoothness of the resulting envelope depends both on the smoothness of the motion and smoothness of the tool. While the motions of the tool are typically required to be at least C2, the tools are frequently only C0 continuous, which results in discontinuous envelopes. In this work, we classify a family of instantaneous motions that, in spite of only C0 continuous shape of the tool, result in C0 continuous envelopes. We show that such motions are flexible enough to follow a free-form surface, preserving tangential contact between the tool and surface along two points, therefore having applications in shape slot milling or in a semi-finishing stage of 5-axis flank machining. We also show that C1 tools and motions still can generate smooth envelopes.

Towards [formula omitted]-Continuous Multi-Strip Path-Planning for 5-Axis Flank CNC Machining of Free-Form Surfaces Using Conical Cutting Tools

Existing flank milling path-planning methods typically lead to tiny gaps or overlaps between neighboring paths, which causes artifacts and imperfections in the workpiece. We propose a new multi-strip path-planning method for 5-axis flank milling of free-form surfaces which targets G1 (tangent-plane) continuity of the neighboring strips along shared boundaries. While for some geometries one cannot achieve G1 continuity and high approximation quality at the same time, our optimization framework offers a good trade-off between machining accuracy in terms of distance error and the G1 connection of neighboring strips. We demonstrate our algorithm on synthetic free-form surfaces as well as on industrial benchmark datasets, showing that we are able to meet fine industrial tolerances and simultaneously significantly reduce the kink angle of adjacent strips, and consequently to improve the surface finish in terms of smoothness.

Tool path generation for 5-axis flank milling of ruled surfaces with optimal cutter locations considering multiple geometric constraints

Ruled surfaces found in engineering parts are often blended with a constraint surface, like the blade surface and hub surface of a centrifugal impeller. It is significant to accurately machine these ruled surfaces in flank milling with interference-free and fairing tool path, while current models in fulfilling these goals are complex and rare. In this paper, a tool path planning method with optimal cutter locations (CLs) is proposed for 5-axis flank milling of ruled surfaces under multiple geometric constraints. To be specific, a concise three-point contact tool positioning model is firstly developed for a cylindrical cutter. Different tool orientations arise when varying the three contact positions and a tool orientation pool with acceptable cutter-surface deviation is constructed using a meta-heuristic algorithm. Fairing angular curves are derived from candidates in this pool, and then curve registration for cutter tip point on each determined tool axis is performed in respect of interference avoidance and geometric smoothness. On this basis, an adaptive interval determination model is developed for deviation control of interpolated cutter locations. This model is designed to be independent of the CL optimization process so that multiple CLs can be planned simultaneously with parallel computing technique. Finally, tests are performed on representative surfaces and the results show the method has advantages over previous meta-heuristic tool path planning approaches in both machining accuracy and computation time, and receives the best comprehensive performance compared to other multi-constrained methods when machining an impeller.

Computational approaches for improving machining precision in five-axis flank milling of spiral bevel gears

Spiral bevel gears are a critical component in mechanical systems that offers high power transmission efficiency between nonparallel axes. The current gear manufacturing, which normally requires specialized machines and cutting tools specific to one gear type, offers limited production flexibility. An effective alternative is to utilize 5-axis computer numerical control milling on general-purpose machine tools. This paper aims to improve the machining precision in the flank milling of spiral bevel gears, particularly the tooth surfaces, using computational approaches. First, a geometric method was developed to approximate the contact path of a gear pair without solving the complex equations in tooth contact analysis. A quantitative measure was introduced to evaluate the contact path deviation from the center curve of the tooth surface. Second, we proposed an optimization scheme for generating tool paths that induce minimal geometrical errors on the finished surface. It employs a metaheuristics-based search algorithm with the errors as an objective in tool path planning. Test results on real gears verified the effectiveness of the proposed scheme. Three measures of the meshing performance, namely the average sampling error, the contact path deviation, and the transmission error, were cross-compared on different gear pairs to examine whether they consistently distinguish the performance rank. This work provides feasible solutions for controlling machining errors in 5-axis flank milling of complex gears.

Screw rotor manufacturing via 5-axis flank CNC machining using conical tools

We propose a new method for 5-axis flank computer numerically controlled (CNC) machining of screw rotors using conical tools. The flanks of screw rotors consist of helical surfaces, which predetermines the motion of the milling tool and reduces the search space for tool positioning to only 4-parametric family, which allows a quick search for good initial positions of a given conical tool. We initialize the search by looking at second order line contact between the tool and the helical flank of the rotor. Several positions of the tool are found, covering major part of the flank of the rotor, followed by global optimization that further reduces the tool-surface error and makes sure that there are no gaps between neighboring sweeps of the tool. We demonstrate our approach on several benchmark screw rotors, showing that our approach meets fine industrial tolerances with only few sweeps of the tool.

An efficient prediction method for the dynamic deformation of thin-walled parts in flank milling

Severe deformation may occur in the flank milling of thin-walled parts due to their low rigidity. Considering the varying stiffness resulting from the moving cutting force and the material removal effect, finite element-based methods have been developed to compute the deformation and generate compensated tool paths. However, they are time-consuming since they require solving the full-scale deformation equation at each cutting location. Therefore, an efficient deformation prediction method is firstly proposed in this study, in which the workpiece stiffness matrix is reduced and dynamically modified to avoid re-meshing meanwhile decreasing the computational scales of the solving process. Then, considering the coupling effect between the compensation value and the deformation error, a compensation strategy without the iteration process is developed to obtain the compensation value with high accuracy and efficiency. The flank milling of four comparison sets of thin-walled aluminum alloy blocks was conducted to validate the proposed method. The experiment results revealed that the proposed method obtained similar accuracy to the finite element methods, but cost less than 62.0% of their computational time. And the machining error ranges of four comparison sets were reduced by more than 58.7% after compensation. The proposed method shows great potential for efficiency and accuracy improvement in the 5-axis flank milling of thin-walled freeform surface parts. • A novel deformation prediction method for the milling of thin-walled parts is proposed to improve computational efficiency. • Compared with other FEM-based methods, the proposed method obtains similar accuracy but greatly decreases computation time. • Considering the coupling effect between the compensation values, a compensation strategy without iterations is developed. • The proposed method is validated through milling experiments, in which the machining errors were greatly reduced.

A High-Accuracy Tool Path Generation (HATPG) Method for 5-Axis Flank Milling of Ruled Surfaces with a Conical Cutter Based on Instantaneous Envelope Surface Modelling

In this paper, a novel framework of generating high-accuracy tool path for 5-axis flank milling of ruled surfaces with a conical cutter is developed by designing the instantaneous envelope surface of each planned cutter location (CL). Based on the analysis of the envelope theory, the instantaneous envelope profile of a selected cutter is only affected by the first-order derivation of the cutter’s motion, i.e. tangent vectors of the tool path. This property reveals an interesting fact that characteristic points on an envelope surface can be controlled via path tangents, thus laying the foundation for accurately evaluating the machining error at a single cutter location. On this basis, a simple yet robust method, called rotations for three-point offset (RTPO) method is first proposed to position a conical cutter to have at least three contact points with a ruled surface. Path tangents optimization is then performed to minimize the geometric deviation between the characteristic points and the ruled surface, followed by fine-tuning of the tool axis with a differential rigid motion. Both path tangent optimization and tool axis tuning are formulated as linear program problems, and the optimal cutter location with path tangents is determined by solving them repetitively. Finally, accurate tool path for conical cutter flank milling is generated with curve registration algorithms that interpolate the planned points and tangents. Examples are provided to validate the proposed method, and one can see high-accuracy flank milling paths can be planned point-by-point without subsequent optimization.

Curve-guided 5-axis CNC flank milling of free-form surfaces using custom-shaped tools

A new method for 5-axis flank milling of free-form surfaces is proposed. Existing flank milling path-planning methods typically use on-market milling tools whose shape is cylindrical or conical, and is therefore not well-suited for meeting fine tolerances for manufacturing of benchmark free-form surfaces like turbine blades, gears, or blisks. In contrast, our optimization-based framework incorporates the shape of the tool into the optimization cycle and looks not only for the milling paths, but also for the shape of the tool itself. Given a free-form reference surface and a guiding path that roughly indicates the motion of the milling tool, tangential movability of quadruplets of spheres centered along a straight line is analyzed to indicate possible shapes and their motions. This results in G1 Hermite data in the space of rigid body motions that are interpolated and further optimized, both in terms of the motion and the shape of the milling tool itself. We demonstrate our algorithm on synthetic free-form surfaces and industrial benchmark datasets, showing that the use of custom-shaped tools is capable of meeting fine industrial tolerances and outperforms the use of classical, on-market tools.

5-axis double-flank CNC machining of spiral bevel gears via custom-shaped tools\u2014Part II: physical validations and experiments

Recently, a new methodology for 5-axis flank computer numerically controlled (CNC) machining, called double-flank machining, has been introduced (see “5-axis double-flank CNC machining of spiral bevel gears via custom-shaped milling tools—Part I: Modeling and simulation”). Certain geometries, such as curved teeth of spiral bevel gear, admit this approach where the machining tool has tangential contact with the material block on two sides, yielding a more efficient variant of flank machining. To achieve high machining accuracy, the path-planning algorithm, however, does not look only for the path of the tool, but also for the shape of the tool itself. The proposed approach is validated by series of physical experiments using an abrasive custom-shaped tool specifically designed for a particular type of a spiral bevel gear. The potential of this new methodology is shown in the semifinishing stage of gear manufacturing, where it outperforms traditional ball end milling by an order of magnitude in terms of machining time, while keeping, or even improving, the machining error.

Manufacturing of Screw Rotors Via 5-axis Double-Flank CNC Machining

We investigate a recently introduced methodology for 5-axis flank computer numerically controlled (CNC) machining, called double-flank milling (Bo et al., 2020). We show that screw rotors are well suited for this manufacturing approach where the milling tool possesses tangential contact with the material block on two sides, yielding a more efficient variant of traditional flank milling. While the tool’s motion is determined as a helical motion, the shape of the tool and its orientation with respect to the helical axis are unknowns in our optimization-based approach. We demonstrate our approach on several rotor benchmark examples where the pairs of envelopes of a custom-shaped tool meet high machining accuracy.

5-axis double-flank CNC machining of spiral bevel gears via custom-shaped milling tools — Part I: Modeling and simulation

A new category of 5-axis flank computer numerically controlled (CNC) machining, called double-flank, is presented. Instead of using a predefined set of milling tools, we use the shape of the milling tool as a free parameter in our optimization-based approach and, for a given input free-form (NURBS) surface, compute a custom-shaped tool that admits highly-accurate machining. Aimed at curved narrow regions where the tool may have double tangential contact with the reference surface, like spiral bevel gears, the initial trajectory of the milling tool is estimated by fitting a ruled surface to the self-bisector of the reference surface. The shape of the tool and its motion then both undergo global optimization that seeks high approximation quality between the input free-form surface and its envelope approximation, fairness of the motion and the tool, and prevents overcutting. That is, our double-flank machining is meant for the semi-finishing stage and therefore the envelope of the motion is, by construction, penetration-free with the references surface. Our algorithm is validated by a commercial path-finding software and the prototype of the tool for a specific gear model is 3D printed.

On initialization of milling paths for 5-axis flank CNC machining of free-form surfaces with general milling tools

We propose a path-planning algorithm for 5-axis flank CNC machining with general tools of varying curvature. Our approach generalizes the initialization strategy introduced for conical tools Bo et al. (2017) to arbitrary milling tools. Given a free-form (NURBS) surface and a rotational milling tool, we look for its motion in 3D to approximate the input reference surface within a given tolerance. We show that for a general shape of the milling tool, there exist locally and generically four 3D directions in which the point-surface distance follows the shape of the tool up to second order. These directions form a 3D multi-valued vector field and its integration gives rise to a set of integral curves. Among these integral curves, we seek straight line segments that correspond to good initial positions of the axes of the milling tool. We validate our method against synthetic examples with known exact solutions and, on industrial datasets, we detect approximate solutions that meet fine machining tolerances. We also demonstrate applicability of our method for efficient flank milling of convex regions that is not possible using traditional conical tools.

Optimized tool path planning for five-axis flank milling of ruled surfaces using geometric decomposition strategy and multi-population harmony search algorithm

Tool path planning is a key to ensure high machining quality and productivity in 5-axis flank milling of ruled surfaces. Previous studies have shown that optimization-driven tool path planning can effectively reduce the geometrical errors on the finished surface. However, to solve the corresponding optimization problem is a challenging task involving a large number of decision variables. This paper proposes a novel approach to generating optimized tool path for 5-axis flank finishing cut based on a geometric decomposition strategy and multi-population harmony search algorithm. The proposed approach geometrically divides the surface to be machined into a number of segments. The tool paths on those sub-surfaces are independently optimized by the multi-population harmony search algorithm. Individual tool paths are then combined together to form a complete one. The test results of representative surfaces show that the proposed approach produces higher machining precision with less computational time than compared previous methods. And the computational time is further reduced by Message passing interface based parallel computing techniques. A detailed analysis is conducted to characterize how the number of divisions affects the optimization results. And the proposed approach also shows good scalability with the increasing number of cutter locations.

Highly accurate 5-axis flank CNC machining with conical tools

A new method for 5-axis flank computer numerically controlled (CNC) machining is proposed. A set of tappered ball-end-mill tools (aka conical milling tools) is given as the input and the flank milling paths within user-defined tolerance are returned. Thespace of lines that admit tangential motion of an associated truncated cone along a general, doubly curved, free-form surface is explored. These lines serve as discrete positions of conical axes in 3D space. Spline surface fitting is used to generate a ruled surface that represents a single continuous sweep of a rigid conical milling tool. An optimization-based approach is then applied to globally minimize the error between the design surface and the conical envelope. The milling simulations are validated with physical experiments on two benchmark industrial datasets, reducing significantly the execution times while preserving or even reducing the milling error when compared to the state-of-the-art industrial software.

A solid-analytical-based model for extracting cutter-workpiece engagement in 5-axis flank machining

5-axis flank milling is applied extensively in aerospace, die-molds, and automotive industries because of high efficient material removal rate. Commercial CAM software can only simulate the tool path and collision at present, but cannot handle with cutting force during cutting process due to the variable geometrical cutter workpiece engagement (CWE) region of 5-axis milling. This paper presents a novel solid analytical model for extracting the CWE maps. The CWE is obtained analytically by performing Boolean operations between the cutter and in-process-workpiece (IPW) at any given cutter location (CL) point, instead of using the cutter and the removal volume. The proposed process simulation method could identify the CWE efficiently and precisely for general cutting tools. Finally, the CWE boundaries are mapped from a 3D space into a 2D plane defined by the immersion angle and the axial depth of a given cutter. The proposed solution can be easily integrated into the CAM software for predicting milling force and optimizing parameters in 5-axis milling.

Initial Tool Orientation Set-up for 5-Axis Flank Milling Based on Faceted Models

One of the factors affecting the effectiveness of machining time of 5-axis miling is the method being used. By using flank milling method, as one of the optimized processes to make a workpiece, the time required for the process becomes shorter.This research is aimed at developing the method for determining the initial orientation of the tool for a sculptured surface on the basis of faceted model. By determining cc-point as the basis for positioning the tool on the surface of the workpiece, the cutting direction is formed from the nearest cc-point in the XY flat plane direction of the faceted model at the spatial coordinate. The positioning of the tool is initially based on the Local Coordinate System developed by the cross product between the normal vector n at each cc-point and cutting direction vector F from one cc-point to the other. The cross product resulted is a tangent vector T of the plane formed from the normal vector and cutting direction. The orientation of the tool is formed and defined by an inclination angle ( α ) and a screw angle ( β ). Maximizing the cutting volume and avoiding gouging at each cc-point during the flank milling are carried out through optimal adjustment of these two rotational angles. Furthermore, when the adjustment of rotational angles cannot resolve the gouging, appropriate tool lifting along the normal vector is conductedhis method is very much applicable for flank milling having the basis of data in the form of faceted models.

Towards efficient 5-axis flank CNC machining of free-form surfaces via fitting envelopes of surfaces of revolution

We introduce a new method that approximates free-form surfaces by envelopes of one-parameter motions of surfaces of revolution. In the context of 5-axis computer numerically controlled (CNC) machining, we propose a flank machining methodology which is a preferable scallop-free scenario when the milling tool and the machined free-form surface meet tangentially along a smooth curve. We seek both an optimal shape of the milling tool as well as its optimal path in 3D space and propose an optimization based framework where these entities are the unknowns. We propose two initialization strategies where the first one requires a user’s intervention only by setting the initial position of the milling tool while the second one enables to prescribe a preferable tool-path. We present several examples showing that the proposed method recovers exact envelopes, including semi-envelopes and incomplete data, and for general free-form objects it detects envelope sub-patches.

Iterative optimization of tool path planning in 5-axis flank milling of ruled surfaces by integrating sampling techniques

Simultaneous adjustment of all cutter locations in a tool path using meta-heuristic algorithms provides a systematic approach to reducing machining errors in 5-axis flank machining of ruled surfaces. However, these algorithms experienced unsatisfactory quality of optimal solutions and lengthy search time in high-dimensional search space. To solve these problems, we propose an iterative optimization scheme that progressively simplifies solution space by sampling techniques. Akaike information criterion (AIC) is used to screen significant factors from sampling data. An electromagnetism-like mechanism (EM) algorithm searches through a simplified solution space constructed only using these factors. An iteration process consisting of such sampling, screening, and searching steps repeats several times until final optimal solutions are obtained. Test results of representative surfaces validate the effectiveness of the proposed scheme. Both solution quality and search efficiency are improved comparing to those produced by previous studies. This work enhances the practicality of optimization-driven tool path planning in 5-axis flank machining.

Tool Path Generation Method for Five-axis Flank Milling of Corner by Considering Dynamic Characteristics of Machine Tool

During the corner machining process of 5-axis flank milling, the sharp change of tool path and tool orientation may lead to a dramatic increase of the milling force and tool vibration, which gravely impacts the machining quality. In order to address this issue, a 5-axis flank milling tool path generation method for corners by considering the dynamic characteristics of machine tool is presented in this paper. To be specific, firstly, the allowance information model of corner is built according to the part model and roughing information. Secondly, the tool trajectory based on clothoid curve and milling force constraint is optimized. And then, the tool orientation based on tool trajectories is optimized. Finally, the 5-axis flank milling tool path is generated by considering the dynamic characteristics of machine tool and the milling force constraint. The remaining materials of corner can be removed uniformly using the proposed tool path, and the curvature of the tool path is continuous. Simulation results show that the machined surface of corner is smooth, and the proposed tool path is suitable for corner machining.

An accurate prediction method of cutting forces in 5-axis flank milling of sculptured surface

The instantaneous uncut chip thickness and entry/exit angle of cutter/workpiece engagement continuously vary with tool path and workpiece geometry in 5-axis flank milling of sculptured surface, which results in the obvious time-varying characteristic for consecutive cutting forces. An accurate prediction method for cutting force in 5-axis flank milling of sculptured surface is proposed in this paper. Comprehensively considering curved tool path and actual tool motion process with cutter runout (offset and inclination) effects, an accurate representation model for instantaneous uncut chip thickness during cutter/workpiece engaging in 5-axis flank milling is presented firstly, which can reach a higher accuracy and efficiency with the aid of linear iteration process than the methods published. Then, based on the thin plate milling experiments, an efficient calibration procedure for cutter runout parameters and specific cutting force coefficients is given and further verified in practice. Finally, a series of validation experiments are conducted under different cutting conditions, and the results reveal that there is a very good agreement between the experimental and simulation data both in shape and magnitude and prove the effectiveness and accuracy of the proposed method.