5-axis Sculptured Surface Machining Research Articles

Empirical Models for Surface Roughness and Topography in 5-Axis Milling Based on Analysis of Lead Angle and Curvature Radius of Sculptured Surfaces

The orientation of the tool axis and the variable curvature of the machined profile of a sculptured surface have a significant impact on the roughness and topography of the surface in the process of 5-axis milling by means of a toroidal milling cutter. The selection of the orientation of the toroidal milling cutter axis relative to the radius of curvature of the machined surface profile is very important as it can provide a better surface quality and an even distribution of roughness parameters. In this paper, an attempt to carry out model tests to obtain mathematical relationships was made. These relationships were to determine the impact of the tool axis orientation and the variable curvature radius of the machined profile on the surface roughness and its topography in the 5-axis milling process of sculptured surfaces. The tests were conducted on an example of a turbine blade made of Inconel 718 alloy. A measurable effect of the work undertaken was the development of model relationships that can be applied in specialized modules of CAM (Computer Aided Manufacturing) systems supporting the programming of 5-axis machining of sculptured surfaces. The models developed will also make it possible to obtain an evenly distributed roughness on the machined sculptured surface, especially on the surface of the turbine blades of the Inconel 718 alloy, as indicated by the results of the tests carried out.

A new approach for predicting wear overlap geometry in ball end finish milling

The inclination angles of sculptured surface and tilting angles of 5-axis machining change cutting time distributions (CTD) on cutting contact (CC) points. The models of element wear (EW) function of the CTD on each CC points are overlapped to form wear overlap (WO) geometry. However, the WO geometry has not been taken into account in most current tool wear models. This paper proposes a new approach for modeling of the WO geometry associated with the overlapping zones in the 5-axis machining of sculptured surfaces. The EWs in response to CTD at each CC points are modeled using probability density function. The EW is changed to the linear function of time by deforming the tool wear unit. Afterward, for each overlapping point, the WO value is calculated by using the method of the linear addition of linearized EWs. Then, the WO geometry is obtained by the inverse deformation of the unit. The proposed approach is demonstrated and validated through a case study. The predictions of WO geometry present good accordance with experimental observations in constant tilting angle and flat convex surface finish milling process.

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.

Evaluation of 3- and 5-axis sculptured surface machining in CAM environment through design of experiments

Sculptured surface machining (SSM) is an operation widely applied to several industrial fields such as aerospace, automotive and mould/die. The number of the parameters and strategies involved to program such machining operations can be enormously large owing to surface complexity and advanced design features. This study focuses on the examination of machining strategies and related parameters for the assessment of roughing and finishing stages. A fractional factorial design implementing an L27 Taguchi orthogonal array (OA) was established to conduct machining experiments with the use of a computer-aided manufacturing (CAM) software. Fractional factorial design specifics involve the statistical elimination of unimportant parameters, thus reducing experimental runs without the loss of useful information. Two scenarios were considered to machine a sculptured part; one involving 3-axis roughing/3-axis finish machining experiments and the other one involving 3-axis roughing/5-axis finish machining experiments. Roughing operation was common for both scenarios. The problem was subjected to discrete technological constraints to reflect the actual industrial status. For each machining phase, two quality objectives reflecting productivity and part quality were determined. Roughing experiments were tested to minimise machining time and remaining volume, whilst finishing experiments were subjected to minimise machining time and surface deviation between the designed and the machined 3D model. Quality characteristics were properly weighted to formulate a single objective criterion for both machining phases. Results indicated that DOE applied to CAM software, enables NC programmers to have a clear understanding about the influence of process parameters for SSM operations, thus generating efficient toolpaths to improve productivity, part quality and process efficiency. Practically the work contributes to machining improvement by through the proposition of machining experimentation methods using safe and useful platforms such as CAM systems; the investigation of approaches to avoid problem oversimplification mainly when large number of machining parameters should be exploited and the evaluation of quality criteria which allow their assessment directly form CAM software.

Study on Methods for Calculating Tool Position Error Distribution during 5-Axis Machining of Sculptured Surfaces

With the continuous improvement of the calculation speed of computer, tool positioning methods based on numerical calculation in five-axis NC programming will play a greater role. First, this paper introduces three numerical methods for calculating tool position error distribution between a torus cutter and design surface in 5-axis machining of sculptured surfaces, namely a method for discretizing design surface, a method for discretizing the torus central circle, and a longitude method. At the same time, the detailed calculating steps are also given. An example of a cylindrical surface machined with torus tool is then conducted to compare and analyze the calculation accuracy and efficiency of the above methods. Results obtained show that the calculating deviation for computing tool position error distribution using the method for discretizing the torus central circle is minimum, while that using another two methods are larger; the calculation time of the method for discretizing the torus central circle is shortest, while that of the longitude method is longest; within the given programming tolerance, the machining strip widths calculated by the above methods are appropriately same, and the maximum deviation of actual machining strip width is within 2% of the theoretical value.

Local Gouge Detection Algorithm for 5-Axis Sculptured Surface Machining Using the Toroidal Cutter

Based on the geometrical property of the toroidal cutter, an improved local gouge detection method for 5-axis sculptured surface machining was presented here. By alternately taking full advantage of point projection principles on curve and surface, the minimum distance between the circular curve of the toroidal cutter and the design surface was firstly calculated. Then the local gouge detection was accomplished through comparing the minimum distance with the corner radius of the toroidal cutter. The maximum interference quantity required for correction was also gotton. Results of an example showed the new method was correct and stable.

Tool Positioning Algorithm Based on Smooth Tool Paths for 5-axis Machining of Sculptured Surfaces

The current research of the 5-axis tool positioning algorithm mainly focuses on searching the local optimal tool position without gouging and interference at a cutter contact(CC) point, while not considering the smoothness and continuity of a whole tool path. When the surface curvature varies significantly, a local abrupt change of tool paths will happen. The abrupt change has a great influence on surface machining quality. In order to keep generated tool paths smooth and continuous, a five-axis tool positioning algorithm based on smooth tool paths is presented. Firstly, the inclination angle, the tilt angle and offset distance of the tool at a CC point are used as design variables, and the machining strip width is used as an objective function, an optimization model of a local tool positioning algorithm is thus established. Then, a vector equation of tool path is derived by using the above optimization model. By analyzing the equation, the main factors affecting the tool path quality are obtained. Finally, a new tool position optimization model is established, and the detailed process of tool position optimization is also given. An experiment is conducted to machine an aircraft turbine blade by using the proposed algorithm on a 5-axis blade grinding machine, and the machined blade surface is measured with a coordinate measuring machine(CMM). Experimental and measured results show that the proposed algorithm can ensure tool paths are smooth and continuous, improve the tool path quality, avoid the local abrupt change of tool paths, and enhance machining quality and machining efficiency of sculptured surfaces.

Advances in Tool Path Planning Techniques for 5-axis Machining of Sculptured Surfaces

Five-axis numerical control machining is an effective means to improve the machining quality and efficiency of the sculptured surface.However,the complexities of the sculptured surface shape and the 5-axis machine tool movement make it very difficult to plan the tool paths.Aiming at the key techniques in the field of end milling,flank milling and collision analysis of 5-axis sculptured surface machining,the current research progresses of 5-axis tool path planning for sculptured surfaces machining are summarized.In view of the engineering practicability requirement,the deficiencies existing in the current research are analyzed.It is pointed out that the current research achievements cannot completely satisfy the engineering application in respect of universally, stability and validity,and that the research of the tool path planning for 5-axis sculptured surface machining should proceed from the viewpoint of three dimensions,and the geometrical meshing relationship between the cutter and the sculptured surface should be researched in a wider cutter influence space.Meanwhile,the kinematics and dynamics characteristics of 5-axis machine tool must be taken into account during the tool path planning process in order to achieve high speed and efficient running of 5-axis machine tool.

Quadric method for cutter orientation in five-axis sculptured surface machining

Existing orientation strategies in 5-axis sculptured surface machining mostly limit the cutter to incline in one direction and lack an effective approach to assess the orientation. This paper presents the quadric method (QM) that exploits fully the two orientation angles to maximise the machining efficiency at a cutter contact point. The geometric construction assumes that the local shape of a sculptured surface can be suitably approximated by two quadrics. An upper quadric lying above the surface is used to orient the cutter, and a lower quadric lying below the surface is used to evaluate machined strip width. Then, the cutter orientation is optimised with respect to the width and is guaranteed to give no gouging. Both flat-end cutter and fillet-end cutter are considered. Simulated examples demonstrate the improved machining efficiency of the QM over current published methods.

Five-Axis High Speed Machining of Sculptured Surfaces by Surface-Based NURBS Path Interpolation

AbstractThis paper presents a new surface-based NURBS path interpolation for 5-axis high speed machining (HSM) of sculptured surfaces. Detailed formulation of the new time-parameter NURBS path interpolation is proposed to convert the NURBS part surface into time-variable parameterized tool paths for 5-axis sculptured surface machining. Based on the machine configurations, the surfacebased NURBS path interpolation directly derives the pivot point location and the spindle orientation to control the machine motion. With the proposed new method, the traditional chordal and linearization deviation errors in 5-axis NC machining can be reduced. Computer implementations and illustrative examples are also presented in this paper. The presented techniques can be used in the CAD/CAM systems and the NC controllers for 5-axis high speed machining of sculptured surfaces.

Third-order local contact and application in 5-axis machining of sculptured surfaces

In order to increase the efficiency in the machining of the sculptured surfaces, the contact principle of differential geometry is applied to the 5-axis NC machining; The best contact condition between tool and the surfaces is researched. Through analysis the contact degree of the intersection line of the cutter and the surfaces is known. In comparison to previous studies, the theory is more restricted and accurate by going beyond the second-order parameters into the third-order, suiting both the primary surfaces of analytical geometry and the computer-generated surfaces of the computation geometry. It has definite procedure of calculation, and the equations are easy to solve. The thought process is very clear: First, suppose that there is a surface of third-order, the coefficients of which are arbitrary; Then find out the best posture of the circle in order that the circle and the surface will most closely contact with each other at the origin position; Finally, develop the surface into a third-order surface at every point of machining and employ the results mentioned above to find the best cutter posture at every point of machining. As a result, the equations are easy to solve, and the concept is clear.

Swept Tool Envelope and Machining Potential Field for 5-Axis Sculptured Surface Machining

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Interference-free tool path generation for 5-axis sculptured surface machining using rational Bézier motions of a flat-end cutter

This paper presents a new approach that uses rational Bézier motions to generate 5-axis tool path for sculptured surface machining (finish cut) with a flat-end cutter. By using dual quaternion to represent a spatial displacement, the representation of kinematic motions for the cutter bottom circle of the flat-end cutter is formulated. Based on that, a new approach for tool path generation using rational Bézier cutter motions is described, in which key issues such as interference avoidance and surface accuracy requirement are addressed. First, a set of cutter contact points on an iso-parametric curve of the designed surface is obtained based on a given fitting tolerance. The associated cutter locations (CLs) are then obtained by finding the suitable cutter orientations that avoid any gouging. The conversion from the CLs to dual quaternion representation is carried out and the rational Bézier dual quaternion curve for cutter motion is generated. The entire tool path is therefore established based on the cutter undergoing the rational Bézier motion. Next, the whole tool path is checked to find (1) if there is any interference between the cutter and the designed surface, and (2) whether the deviation between the surface generated by the cutter motion and the designed surface is larger than the given tolerance. The problematic CLs, which cause either gouging or accuracy problem, are then modified. The process of tool path checking → CLs modification → tool path regeneration continues until the whole tool path is interference-free and satisfies the accuracy requirement. Furthermore, a more accurate representation of the effective cutting shape is proposed, which is used to evaluate the scallop height between adjacent tool paths. A method for constructing the adjacent tool path has been developed by considering the allowable scallop height. Finally, computer implementation and an illustrative example are presented to demonstrate the efficacy of the approach.

Tool tip gouging avoidance and optimal tool positioning for 5-axis sculptured surface machining

This article deals with locally optimal cutting positions and cutting directions for tool tip gouging avoidance in 5-axis sculptured surface machining. In order to measure the quality of tool positioning, this paper suggests a new concept of 'machined region width', which does not have the drawbacks of 'machined strip width'. The method evaluates the optimal cutting position of a flat endmill or toroidal endmill, where optimality is with respect to the avoidance of tool tip gouging. It is based on a second-order Taylor approximation of the design surface and multipoint tool positioning. The implementation and some illustrative examples are discussed.

Optimizing tool orientations for 5-axis machining by configuration-space search method

This paper presents a methodology and algorithms of optimizing and smoothing the tool orientation control for 5-axis sculptured surface machining. A searching method in the machining configuration space (C-space) is proposed to find the optimal tool orientation by considering the local gouging, rear gouging and global tool collision in machining. Based on the machined surface error analysis, a boundary search method is developed first to find a set of feasible tool orientations in the C-space to eliminate gouging and collision. By using the minimum cusp height as the objective function, we first determine the locally optimal tool orientation in the C-space to minimize the machined surface error. Considering the adjacent part geometry and the alternative feasible tool orientations in the C-space, tool orientations are then globally optimized and smoothed to minimize the dramatic change of tool orientation during machining. The developed method can be used to automate the planning and programming of tool path generation for high performance 5-axis sculptured surface machining. Computer implementation and examples are also provided in the paper.

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.

Locally optimal cutting positions for 5-axis sculptured surface machining

The paper presents a local condition for collision-free 5-axis milling of sculptured surfaces. We consider cutter positions, which guarantee local gouging avoidance. This can replace concepts such as ‘cutting profile’ or ‘effective cutting shape’ which are of approximate nature. Based on second order approximations of the machined strip width, we also present locally optimal cutting positions for cutting directions.

Manufacturability Analysis for a Sculptured Surface Using Visibility Cone Computation

This paper presents a general algorithm to obtain a feasible tool-approach direction for sculptured surface machining based on convex analysis. The visibility cone which represents the aggregate of all visible directions is constructed to describe geometric constraints. Combined with the convex hull computation algorithm, a detailed procedure for computing the visibility cone has been developed. The visibility cone can be used as an effective tool for manufacturability analysis of the sculptured surface when applied to CNC machining tool-path planning. After the visibility cone is acquired, tool orientation can be adjusted to adapt itself to the local geometry of the sculptured surface at each cut contact position. The proposed methodology can be applied to computer-aided planning and programming of cutter-path generation for 5-axis sculptured-surface machining.

Non-isoparametric tool path planning by machining strip evaluation for 5-axis sculptured surface machining

Presented in this paper is a new approach to 5-axis NC tool path generation for sculptured surface machining. Techniques of feasible machining strip evaluation are used for non-isoparametric 5-axis tool path generation. A searching algorithm is proposed to find the parameter increments of adjacent cutter locations along orthogonal path intervals for optimal non-isoparametric path generation. Compared to the use of the smallest path interval by the traditional constant parametric path planning, the proposed methodology can generate efficient tool paths for sculptured surface machining by reducing the redundant overlapping between adjacent tool paths. The proposed methodology includes three steps: (1) evaluating feasible machining strip, (2) solving parameter increments (Δ u, Δ v) along orthogonal path intervals, and (3) searching for adjacent non-isoparametric cutter locations. The techniques presented in this paper can be used to improve 5-axis machined surface quality and to automate the non-isoparametric cutter path generation for CAD/CAM systems.

Automatic cutter selection for 5-axis sculptured surface machining

In 5-axis machining, simultaneous change of tool orientation during machining affects the effective cutter shape, thus making the cutter selection difficult. In this paper, a maximum effective cutting radius approach is proposed to solve the cutter selection problem for multi-axis machining. The effective cutting radius of a tool is represented by a function of its physical tool size and the tool orientation angles, the incline angle λand the tilt angle ω. Optimal cutter selection is determined by geometric evaluation through the maximum effective cutting radius approach. A boundary-based approach for roughing cutter selection is also briefly discussed. The proposed methodology can be used to select cutters for the 3-, 4-, and 5-axis sculptured surface machining.