Machining Strip Width Research Articles

A Multi-Scale Tool Orientation Generation Method for Freeform Surface Machining with Bull-Nose Tool.

Free-form surface parts are widely used in industries, and they consist of intricate 3D surfaces such as molds, impellers, and turbine blades that possess complex geometrical contours and demand high precision. Proper tool orientation is crucial for ensuring the efficiency and accuracy of five-axis computer numerical control (CNC) machining. Multi-scale methods have received much attention and have been widely used in various fields. They have been proven to be instrumental and can obtain fruitful outcomes. Ongoing research on multi-scale tool orientation generation methods, which aim to acquire tool orientations that satisfy both macro- and micro-scale requirements, is significantly important for improving the machining quality of workpiece surfaces. This paper proposes a multi-scale tool orientation generation method that considers both the machining strip width and roughness scales. This method also ensures a smooth tool orientation and avoids interference in the machining process. First, the correlation between the tool orientation and rotational axis is analyzed, and feasible area calculation and tool orientation adjustment methods are introduced. Then, the paper introduces the calculation method for machining strip widths on the macro-scale and the roughness calculation method on the micro-scale. Besides, tool orientation adjustment methods for both scales are proposed. Next, a multi-scale tool orientation generation method is developed to generate tool orientations that meet the macro- and micro-scale requirements. Finally, to verify the effectiveness of the proposed multi-scale tool orientation generation method, it is applied to the machining of a free-form surface. Experimental verification results have shown that the tool orientation generated by the proposed method can obtain the expected machining strip width and roughness, meeting both macro- and micro-scale requirements. Therefore, this method has significant potential for engineering applications.

Numerical implementation of drop spin and tilt method for five-axis tool positioning for tensor product surfaces

This paper presents an extension of multipoint machining technique, called the Drop Spin and Tilt (DST) method, that spins the tool on two axes, allowing for the generation of multiple contact points at varying distances around the first point of contact. The multiple DST second points of contact were used to manually generate a toolpath with uniform spacing between the two points of contact. The original DST method used a symbolic algebra package to position the tool on a bi-quadratic surface; our extension is a numerical solution that allows positioning a toroidal tool on a tensor product Bézier surface, which we tested on bi-degrees 2, 3, 4, and 5. On the three bicubic surfaces we tested, the average number of initial seeds for our numerical method was less than 5 across all three surfaces, and the average number of Newton iterations was less than 20 except when the curvature of the tool closely matches the local surface curvature (in which case more iterations were required). Furthermore, we investigate the spread of possible second points of contact as the tool is spun around these two axes, demonstrating the feasibility of using the method to control the machining strip width.

A Tool Tilt Angle Calculation Method in 5-axis Flat-end Milling for Free Surface Machining

This paper proposes a method for calculating the tilt angle of the tool and the machining strip width when the tool is inclined to the feed direction. Tilt angle of the tool and machining strip width are important factors which affect feed rate and machining quality in five-axis flat-end milling for free surface. There are some methods to calculate the tilt angle of the tool in five-axis flat-end milling for free surface, but mathematically complicated algorithm is applied to the calculation of tilt angle of the tool, so it is difficult to apply it in practice. We considered the geometry of the surface and the tool as well as the scallop height to determine the tool tilt angle, thus ensuring the tool to be contacted with the surface at two points. This allows us to calculate the tool tilt angle and the machining strip width by solving quadric equations based on the contact circle. Moreover, tool tilt angle and machining strip width are calculated analytically. Thus the speed of calculation is quick and easy to implement. An experiment of machining on the biquantic B-spline surface was performed and the results show that the proposed method has considerably higher machining efficiency than the CMM.

A region-based tool path generation approach for machining freeform surfaces by applying machining strip width tensor

In freeform surface machining, the cutter should move along the feed directions with maximal machining strip widths (MSW) as much as possible to improve machining efficiency. However, since the optimal feed directions usually vary among different regions over a complex freeform surface, only local optimal machining result could be achieved by most existing tool path generation methods which consider the whole surface as one machining region. This research proposes a tensor-based approach to generate regional tool paths for more globally optimal machining result. A rank-two tensor is first constructed to enable the evaluation of the MSW over the whole feed direction space at the cutter contact point (CCP). To make this MSW tensor usable for generic APT cutters, the concept of effective cutting surface (ECS) is raised. The tensor is then obtained by modeling the geometric approximation between the ECS and the part surface around CCP. A MSW tensor field is then induced over the entire part surface. The regional distribution of the optimal feed directions is associated with the degenerate points within the tensor field. Then, the surface may be divided into several machining regions by constructing inside boundaries starting from the trisector degenerate points. At last, tool paths will be separately calculated in each sub-surface. Since the optimal feed directions in each sub-surface vary continuously, the cutter movements can follow the optimal feed directions closely based on the generated regional tool paths which refer to shorter tool path length and machining time. Two parts with freeform surface are selected from the real industry as test cases and the comparisons to other traditional methods are also provided.

A region-based 3 + 2-axis machining toolpath generation method for freeform surface

Due to the geometric complexity, tool orientations usually change dynamically during freeform surface machining with 5-axis machine tool. As the kinematic performance of the rotary axes is usually weaker than that of the linear axes, the real cutting speed is difficult or even impossible to reach the desired level, which further leads to low machining efficiency. This paper presents a region-based 3 + 2-axis machining toolpath generation method with 5-axis machine tool. The surface is first divided into several preliminary sub-surfaces using K-means clustering algorithm. A post processing procedure is then carried out to optimise the preliminary sub-surfaces to ensure the machinability. For each sub-surface, gouging-/collision-free tool orientations are first calculated and then the optimal combination of the fixed tool orientation and the feed direction is determined by maximising the average machining strip width for toolpath generation. The proposed method is tested by a case surface and the comparisons to some other traditional methods are also provided.

Optimization of machining strip width using effective cutting shape of flat-end cutter for five-axis free-form surface machining

Tool postures of the flat-end cutter can make a huge difference to both machining strip width and machining efficiency in five-axis end milling. Most of current methods evaluate the machining strip width and implement a tool orientation optimization by finding two intersection points between the effective cutting profile of a flat-end cutter and the offset surface profile which represents machined surface. However, real machining strip width and real residual height should be formed between two adjacent cutter contours. As the results, two problems of current methods cannot be avoided: (1) Machining strip width computed on a single cutter location cannot accurately represent the distance between two adjacent tool paths and (2) excessive overlap or larger span length between two adjacent cutter contours leads to unsteady residual height, which causes surface quality differences. In order to solve the above problems, a more suitable method for computing machining strip width is presented and proved in this paper. A flat-end cutter is adopted and the analytical model of effective cutting shape for this kind of tool is constructed firstly. Later, a geometric foundation to achieve optimization is established by investigating the impact of different flat-end cutter postures on the machining strip width. Furthermore, the reasonable strip width is obtained and optimized by implementing an iterative and optimization approach under the given scallop height. A three-dimensional centrifugal compressor blade is used as a numerical example to verify the approach presented in this paper. To prove the superiority of the involved method, the research gives a comparison with UG method with the same cutting parameters. Numerical experiment suggests that machining efficiency of the paper’s method improves by 37.85%. Finally, a machining simulation is performed in the VERICUT software to testify that a uniform error distribution is created.

Dynamics and Stability Prediction of Five-Axis Flat-End Milling

The tool orientation of a flat-end cutter, determined by the lead and tilt angles of the cutter, can be optimized to increase the machining strip width. However, few studies focus on the effects of tool orientation on the five-axis milling process stability with flat-end cutters. Stability prediction starts with cutting force prediction, and the cutting force prediction is affected by the cutter-workpiece engagement (CWE). The engagement geometries occur between the flat-end cutter and the in-process workpiece (IPW) are complicated in five-axis milling, making the stability analysis for five-axis flat-end milling difficult. The robust discrete vector method (DVM) is adopted to identify the CWE for flat-end millings, and it can be extended to apply to general cutter millings. The milling system is then modeled as a two-degrees-of-freedom spring-mass-damper system with the predicted cutting forces. Thereafter, a general formulation for the dynamic milling system is developed considering the regenerative effect and the mode coupling effect simultaneously. Finally, an enhanced numerical integration method (NIM) is developed to predict the stability limits in flat-end milling with different tool orientations. Effectiveness of the strategy is validated by conducting experiments on five-axis flat-end milling.

Variable eccentric distance-based tool path generation for orthogonal turn-milling

This study proposes an algorithm for maximizing strip width in orthogonal turn-milling based on variable eccentric distance. The machining error model is first established based on the local cutting profile at the contact line. The influencing factors of the strip width are then investigated to analyze their features and determine an optimizing strategy. The optimized model for maximum machining strip width is formulated by adopting a variable eccentric distance. Hausdorff distance and Frechet distance are introduced in this study to implement the constraint function of the machining error in the optimized model. The computing procedure is subsequently provided. Simulations and experiments have been conducted to verify the effectiveness of the proposed algorithm.

Preferred feed direction field: A new tool path generation method for efficient sculptured surface machining

This paper presents a new method to generate efficient ball-end milling tool paths for three-axis sculptured surface machining. The fundamental principle of the presented method is to generate the tool paths according to a preferred feed direction (PFD) field derived from the surface to be machined. The PFD at any point on the surface is the feed direction that maximizes the machining strip width. Theoretically, tool paths that always follow the direction of maximum machining strip width at every cutter contact point on the surface would result in shorter overall tool path length. Unfortunately, overlaps of adjacent machining strips commonly exist for tool paths that follow the preferred directions exactly. Such redundant machining can be reduced by iso-scallop tool paths. Nonetheless, iso-scallop tool paths do not in general follow the preferred feed directions. To improve machining efficiency via generating short overall tool path length, the presented method analyzes the PFD field of the surface and segments the surface into distinct regions by identifying the degenerate points and forming their separatrices. The resulting segmented regions are characterized by similar PFD’s and iso-scallop tool paths are then generated for each region to mitigate redundant machining. The developed method has been validated with numerous case studies. The results have shown that the generated tool paths consistently have shorter overall length than those generated by the existing methods.

A tool path generation method for freeform surface machining by introducing the tensor property of machining strip width

Due to the complexity of geometry, the feed direction with maximal machining strip width usually varies among different regions over a freeform surface or a shell of surfaces. However, in most traditional tool path generation methods, the surface is treated as one machining region thus only local optimisation might be achieved. This paper presents a new region-based tool path generation method. To achieve the full effect of the optimal feed direction, a surface is divided into several sub-surface regions before tool path computation. Different from the scalar field representation of the machining strip width, a rank-two tensor field is derived to evaluate the machining strip width using ball end mill. The continuous tensor field is able to represent the machining strip widths in all feed directions at each cutter contact point, except at the boundaries between sub-regions. Critical points where the tensor field is discontinuous are defined and classified. By applying critical points in the freeform surface as the start for constructing inside boundaries, the surface could be accurately divided to such that each region contain continuous distribution of feed directions with maximal machining strip width. As a result, tool paths are generated in each sub-surface separately to achieve better machining efficiency. The proposed method was tested using two freeform surfaces and the comparison to several leading existing tool path generation methods is also provided.

Reducing fluctuation of machining strip width by tool position modification for five-axis NC machining of sculptured surfaces

This paper presents a method to reduce the fluctuation of machining strip width by modifying tool position. When the machining strip width varies rapidly within a tool path, the fluctuation of cutting force brings negative influence on the workpiece and cutter. Furthermore, as the tool path interval is always defined conservatively to avoid undercut, the machined strips of adjacent tool paths have unnecessary amount of overlap. Rapid changing machining strip width usually creates too much overlap at some location, which causes repeated cutting. A method is proposed to modify tool position and reduce the fluctuation of machining strip width. Besides, tilt angle smoothness along the tool path is also taken into account. The computation result of a blade surface verified the validity of the proposed method.

Achieving quasi constant machining strip width in five-axis frontal grinding with toroidal tools

Five-axis frontal grinding has an advantage in finish machining of freeform surface due to high surface accuracy and material removal rate. This article focuses on achieving nearly constant machining strip width with toroidal cutter. To begin with, the initial tool path is generated to realize the maximum machining strip width with fixed yaw angle at each cut contact point and then the verges of machined area convergent to the effective machined area after modifying tool posture. The experimental test shows that the proposed method can obtain quasi constant machining strip width.

Optimising tool positioning for achieving multi-point contact based on symmetrical error distribution curve in sculptured surface machining

The multi-point tool positioning algorithms produce much larger machining strip width than the single-point algorithms and apparently reduce the actual machining time. This paper presents a tool positioning algorithm for multi-point machining of sculptured surface, which is excellent at dealing with both of concave and convex surfaces. The proposed method is based on the middle-point error control (MPEC) method, which means the connection point between cutter and surface corresponds to the middle point of error distribution curve. Usually, only one cut contact (CC) point can be obtained with this method. Thus, the proposed method improved the MPEC method for achieving two CC points. At first, the shape of error distribution curve is investigated, and its asymmetry is evaluated. Secondly, the error distribution curve becomes symmetrical after the cutter is rotated with a roll angle, and the cutter is separated with surface at the same time. Finally, the minimum tilt angle is found, and two CC points are obtained without gouging. Machining experiment is conducted to verify the proposed method, and the result reveals that the machining strip width is increased apparently and the tool position is almost unchanged after the adjustment with proposed method. Simulation, measurement, and analysis are also given in the part of the experiment.

Flat-end cutter orientation on a quadric in five-axis machining

The authors have recently developed methods for cutter orientation and tool path generation in 5-axis sculptured surface machining, where the design surface is approximated locally by a quadric. This paper presents, from a purely geometric perspective, the fundamental theory for optimising the cutter orientation on a quadric, which maximises the machined strip width whilst avoiding local and rear gouging. The analysis focuses on the flat-end cutter which is modelled by a circular cylinder but can be generalised for any fillet-end cutter using an appropriate offset of the design surface and the concept of geometric equivalency. The theory is illustrated by three examples.

Improved Rotary Contact Method for 5-Axis Sculptured Surfaces Machining

The 5-axis tool positioning strategy named rotary contact method (RCM) for sculptured surfaces machining has been developed in our previous paper (Fan et al., 2012, “Rotary Contact Method for 5-Axis Tool Positioning,” Trans. ASME J. Manuf. Sci. Eng., 134(2), p. 021004). The RCM finds the optimal tool positions by rotating the tool backward based on the offset surface, and can generate big machined strip width. However, the RCM can only guarantee a contact point because of the design surface's geometric asymmetry in most cases, which leads to the poor surface quality. To resolve this problem, the improved rotary contact method (IRCM) is developed in this paper. The parametric equation of the circular curve of the toroidal cutter defined by the backward and the sideward tilt angle of the tool is strictly deduced. According to the nested optimization of the two tool's angles, there are two contact points found between the tool's cutting surface and the design surface around the feed direction without gouging. Tool positions investigation, machining simulation and cutting experiment are all performed based on a test surface. The results verify the correctness and effectiveness of the IRCM and show that the IRCM can apparently improve the surface quality compared to the RCM.

Using rotary contact method for 5-axis convex sculptured surfaces machining

The 5-axis tool positioning strategy named rotary contact method (RCM) for sculptured surfaces machining has been developed in our previous paper (Wengang Fan et al., J Manuf Sci E-T ASME 134(2):021004.1-021004.6, 2012). The RCM finds the optimal tool positions by rotating the tool backward based on the offset surface instead of the design surface, and can generate big machined strip width without gouging. However, the RCM only deals with concave sculptured surfaces machining well at present, and the special property of convex sculptured surfaces machining has not been fully exploited. To resolve this problem, the general convex sculptured surfaces machining using the RCM is implemented in this paper. Firstly, the tool position error distribution for different tool feed directions is deeply investigated. It is concluded that the best tool feed direction is collinear with the maximum direction of curvature, which is completely opposite to the case for concave sculptured surfaces machining. Then the relationship between the key parameters in the RCM and the tool position error distribution as well as the tool path generation is totally discussed. Finally, machining simulation and cutting experiment of a convex sculptured surface example are performed. The results show that the RCM can apparently raise the efficiency of manufacturing process by contrast with the algorithm in the software UG for convex sculptured surfaces machining.

New CNC Machining Method for Sculptured Surface Using Non-Ball-End Tools

In current multi-axis CNC manufacture technology, the sculptured surface has to be approximated to simplify its complexity, therefore, the current machining methods can not fully exploit the flexibility of the multi-axis CNC tools and offer the prospect of higher machining efficiency and better machining quality. A new theory (Envelope-Approximation Theory) was presented to generate the sculptured surface by maximizing the machined strip width based on the moving frame. The differential geometry based on the idea of the moving frame was discussed to determine the related motion of the tool and the workpiece. The optimized model of the related motion of the tool was established to enable the envelope of the tool surface approximate to the predesigned surface aiming at the least warping. Simulated examples based on Matlab7.0 demonstrate the improved machining efficiency and precision of the Envelope-Approximation Theory over current published methods.

Isoscallop of Self-Adaptive Tool Orientation with Toroidal Cutter under Optimum Orientation of MCPs

End-milling of free-form surfaces on 5-sxis NC tools is a complex problem which has been studied by a large number of research scientists. When end-milling non-convex surfaces, there is a risk of interference between the tool and the surface. This paper presents a new approach to generate gouging-free tool path for constant scallop-height machining using 5-axis toroidal milling. Based on second-order approximations of the machined strip width, we present locally optimal cutting positions for cutting directions. The largest machined strip width of iso-scallop and the corresponding gouging-avoidance tool orientation are calculated. In the cutter path generation procedures, the master cutter paths have been chosen from the minimum curvature loci of the surface. The tool path generated by this method are also compared with that of the long edge of surface as the MCP, the results of simulation show that the method can yield a reduction in line segments of tool path . Velocity curve and acceleration curve are smoother.

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.

Rotary Contact Method for 5-Axis Tool Positioning

In this paper, a new 5-axis tool positioning algorithm called the rotary contact method (RCM) for open concave surface machining using the toroidal cutter is developed. The RCM comes from the reverse thinking of multipoint machining (MPM) method and apparently distinguishes the traditional tool positioning principles, as it determines the optimal tool positions based on the offset surface instead of the design surface. The basic idea of the RCM is to determine the initial tool location first and then rotate the tool for required contact. The RCM can not only guarantee gouge-free tool positions without the additional local gouge checking and correction process but also effectively produce big machined strip width for open form surface machining just like the MPM. Besides, this new method is simple to implement. Machining simulation was performed to verify the validity of the RCM.