Free-form Surface Machining Research Articles

Investigation of a dynamics-oriented engineering approach to ultraprecision machining of freeform surfaces and its implementation perspectives

In current precision and ultraprecision machining practice, the positioning and control of actuation systems, such as slideways and spindles, are heavily dependent on the use of linear or rotary encoders. However, positioning control is passive because of the lack of direct monitoring and control of the tool and workpiece positions in the dynamic machining process and also because it is assumed that the machining system is rigid and the cutting dynamics are stable. In ultraprecision machining of freeform surfaces using slow tool servo mode in particular, however, account must be taken of the machining dynamics and dynamic synchronization of the cutting tool and workpiece positioning. The important question also arises as to how ultraprecision machining systems can be designed and developed to work better in this application scenario. In this paper, an innovative dynamics-oriented engineering approach is presented for ultraprecision machining of freeform surfaces using slow tool servo mode. The approach is focused on seamless integration of multibody dynamics, cutting forces, and machining dynamics, while targeting the positioning and control of the tool–workpiece loop in the machining system. The positioning and motion control between the cutting tool and workpiece surface are further studied in the presence of interfacial interactions at the tool tip and workpiece surface. The interfacial cutting physics and dynamics are likely to be at the core of in-process monitoring applicable to ultraprecision machining systems. The approach is illustrated using a virtual machining system developed and supported with simulations and experimental trials. Furthermore, the paper provides further explorations and discussion on implementation perspectives of the approach, in combination with case studies, as well as discussing its fundamental and industrial implications.

Force model of freeform surface multi-axis machining with fillet end mill based on analytical contact analysis

In the multi-axis machining of freeform surface, compared with ball end mill, the fillet end mill has higher machining efficiency under the same residual height and has been widely used. As the most important physical quantity in machining process, milling force has always been the focus of research. In this paper, the contact geometry between fillet end mill and freeform surface is analyzed by analytical method, and then the milling force prediction model of multi-axis machining is established. Based on differential discretization, the cutter location point of multi-axis machining of freeform surface is approximate to multi-axis machining of oblique plane, which simplifies the research object. The inclination angle is defined to describe the relationship among cutter axis, feed, and workpiece in cutter coordinate system. The space range of the cutting edge element participating in material cutting is constructed by the swept surface of previous tool path, the to-be machined surface and the feed direction surface, and the in-cut cutting edge is determined by judging the cutting edge element one by one. Considering cutter run-out, the element cutting forces on the cylindrical and fillet surfaces of fillet end mill are derived, and all the element forces within in-cut cutting edge are summed by vector to obtain the overall milling force of fillet end mill. Simulation results show that, compared with the solid method, this contact analysis method between cutter and workpiece can take both efficiency and accuracy into account. In the machining experiment, the measured force and predicted force are consistent in trend and amplitude, which verifies the effectiveness of the milling force prediction model.

Geometry and tool motion planning for curvature adapted CNC machining

CNC machining is the leading subtractive manufacturing technology. Although it is in use since decades, it is far from fully solved and still a rich source for challenging problems in geometric computing. We demonstrate this at hand of 5-axis machining of freeform surfaces, where the degrees of freedom in selecting and moving the cutting tool allow one to adapt the tool motion optimally to the surface to be produced. We aim at a high-quality surface finish, thereby reducing the need for hard-to-control post-machining processes such as grinding and polishing. Our work is based on a careful geometric analysis of curvature-adapted machining via so-called second order line contact between tool and target surface. On the geometric side, this leads to a new continuous transition between "dual" classical results in surface theory concerning osculating circles of surface curves and osculating cones of tangentially circumscribed developable surfaces. Practically, it serves as an effective basis for tool motion planning. Unlike previous approaches to curvature-adapted machining, we solve locally optimal tool positioning and motion planning within a single optimization framework and achieve curvature adaptation even for convex surfaces. This is possible with a toroidal cutter that contains a negatively curved cutting area. The effectiveness of our approach is verified at hand of digital models, simulations and machined parts, including a comparison to results generated with commercial software.

Generation Method of Cutting Tool Paths for High-Speed and High-Quality Machining of Free-Form Surfaces

In general, NC programs for machining free-form surfaces using a computer numerical control (CNC) machine tool are generated using a computer-aided manufacturing (CAM) system. The tool paths (CL data) generated by a CAM system are approximated straight-line segments based on tolerance (allowable error). As a result, the tolerance affects the machining accuracy and time. If the tolerance is set to a small value, the lengths of the segments are shortened, and the machining accuracy is improved. The process in which a CNC machine tool reads and analyzes an NC program and controls the motors requires a minimum processing time of an NC program block (block-processing time). Therefore, if the lengths of the approximated straight-line segments are too small, it will be impossible to reach the indicated feed speed, and the machining time will be longer. In this study, by identifying the block-processing time of a CNC controller and deriving the appropriate length of the approximated straight-line segment based on the block-processing time, a CL data creation method that is capable of high-speed and high-accuracy free-form surface machining is proposed. In addition, experimental verification tests of the method are conducted.

An approximation method combined with conformal transformation for the fast measurement of blade section curves

To realize high-precision machining of free-form blade surfaces, it is necessary to measure and reconstruct the blade morphology several times. Sampling measurements and data compression through free-curve approximation technology are of great benefit in shortening the processing time. A novel B-spline approximation method is proposed in this paper, which can determine a few dominant points based on curvature characteristics to approximate dense and noisy measured points with high precision. We adopt a unique adaptive knot placement strategy combined with a curvature dependent evaluation parameter and a conformal transformation method. This strategy is error-bounded in the initial knot placement, which greatly reduces the time consumed by subsequent iterative insertions. The proposed method shows advantages in approximation accuracy, compression rate, and especially in computational efficiency, in comparison with four traditional knot placement methods. Experiments were carried out and the results show that the dominant point selected by this method can replace the fine measurement results, and the compression rate of the measurement points can reach more than 90%. This method is suitable for the sampling measurement and compression of the data of blades, aircraft wings, and other similar free-form surfaces, and is especially suitable for solving the inefficiency problem caused by repeated measurements made in the process of iterative machining of aero-engine blades.

Recursive algorithm for modeling non-linear etching rates in reactive plasma jet based optical surface machining of borosilicate crown glass

Application-specific optical glass properties are achieved by utilizing complex material compositions. This can be problematic in reactive plasma-assisted deterministic surface processing since a non-volatile surface layer may form depending on the glass composition, which affects the etch rate and thereby the local etching depth. In this investigation, a model algorithm is proposed to tackle some restrictions in applying fluorine-based plasma jet as etching tool utilized for freeform surface machining of optics made of complex glass composition, like borosilicate crown glass (e.g., N-BK7®). In this regard, firstly an analytical model is proposed for estimating the depth-dependent etch rate function. Subsequently, a recursive simulation algorithm is introduced for convolving the derived depth-dependent etch rate function with the given dwell time matrix to simulate a deterministic freeform generation process. By the proposed simulation algorithm, the impeding influence of the residual layer on the reduction of etching depth is computed prior to a real experiment in order to scale the local dwell time to ensure the targeted local removal. Finally, the simulated freeform shape is compared with the corresponding result of an etching experiment to validate the feasibility of the proposed approach.

Milling Force Prediction Model for Five-Axis Machining of Freeform Surface Considering Mesoscopic Size Effect

Abstract The core parts with the characteristic of freeform surface are widely used in the major equipment of various fields. Cutting force is the most important physical quantity in the five-axis CNC machining process of core parts. Not only in micro-milling, but also in macro-milling, there is also an obvious size effect, especially in medium- and high-speed milling, which is frequently ignored. In this paper, the milling force prediction model for five-axis machining of a freeform surface with a ball-end mill considering the mesoscopic size effect is established. Based on the characteristics of cutting thickness in macro-milling, a new dislocation density correction form is proposed, and a new experiment is designed to identify the dislocation density correction coefficient. Therefore, the shear stress calculated in this paper not only reflects the cutting dynamic mechanical characteristics but also considers the mesoscopic size effect. A linear function is proposed to describe the relationship between friction coefficient and cutting speed, cutter rake angle, and cutting thickness. Considering cutter run-out, the micro-element cutting force in the shear zone and plough zone are analyzed. The cutting geometry contact between the freeform surface and the ball-end mill is analyzed analytically by the space limitation method. Finally, the total milling force is obtained by summing all the force vectors of cutting edge micro-elements within the in-cut cutting edge. In the five-axis machining experiment of freeform surface, the theoretically predicted results of milling forces are in good agreement with the measured results in trend and amplitude.

Analytical cut geometry calculation for multi-pass rough milling of a free-form surface machining

This paper presents a simple analytical approach to define cut geometry of multi-pass rough milling during a free-form surface milling. The shape of in-process workpiece surface was identified using the coordinate of corner points that are found in every step of stair-surface. In every instantaneous tool location, the workpiece sections that have possibility intersecting with the cutting edge were identified based on the coordinate of cutter location point. The algorithm was developed for machining using indexable flat end-mill by considering the effect of helix angle to the cut geometry. The proposed method was successfully used to determine the length of cut and generate the shape of cuts. The implementation test also demonstrated that helix angle tends to produce larger cut.The validation of the accuracy was carried out by comparing the length of cut measured using CAD software with those generated by the proposed approach. The results showed that the differences were very small or less than 0.4%. Therefore, it can be taken into conclusion that the method was accurate. The comparison test on computational time was conducted. ABS took only 1.63 second for calculating cut geometry during one tool pass, while Z-mapping method spent 23.21 second. This result proved that ABS is computationally more efficient.

Partition-based five-axis tool path generation for freeform surface machining using a non-spherical tool

Freeform surfaces are widely used in many industries for various purposes, and multi-axis CNC machining is the most adopted method for machining them due to its high accuracy and flexibility. The prevailing type of cutter used in machining freeform surfaces is the so-called ball-end type, which is simply a hemisphere and thus has a constant curvature on the cutter surface. Naturally, for a complex surface with a large deviation in curvature, a cutter shape with variable curvature will be more desirable, as we can adaptively choose a portion of smaller curvature on the cutting edge to machine those relatively flat portions on the surface so to enlarge the cutting width and hence reduce the machining time. Towards this objective, in this paper, we present an algorithm which, given an arbitrary freeform surface to machine and a general non-spherical cutter, will generate a five-axis tool path that will strive to match every cutting point on the surface with a locally optimal tool posture (i.e., the contact point on the cutter surface together with the tool orientation) as well as the corresponding optimal feed direction, while both the local gouging-free and global collision-free constraints and the cusp height requirement are all satisfied. The experimental results in both computer simulation and physical machining are also reported, which confirm that, when compared to using a simple ball-end cutter, by using a non-spherical cutter and adaptively adjusting the contacting tool posture and the feed direction, a large improvement in machining efficiency could be achieved, e.g., as much as 60 % achieved in our experiments.

Dynamic performance test under complicated motion states for five-axis machine tools based on double ballbar

During five-axis CNC machining, the dynamic tracking error caused by imperfect servo dynamic performance is becoming the major factor affecting the accuracy during high-speed and high-precision manufacturing. The double ballbar (DBB) test is one of the commonly used dynamic performance tests, but existing DBB test methods do not have satisfactory test capability for the requirement of complex freeform surface machining. In this paper, on the basis of summarized of dynamic tracking error’s mechanism and characteristics, an improved dynamic performance test based on DBB, which is named the circle-8 test, is proposed. In this test, a provenly efficient RTCP test trajectory is used to rebuild the DBB test process, which includes complex movements of all the five motion axes. To exhibit the improvement of the circle-8 test, this test and the BK3 test of ISO standard, which is considered as a comparison, are conducted in a five-axis machine tool with a tilting rotary table. According to the simulation and experiment results, for common dynamic inaccuracy situations, the circle-8 test always has better sensitivity of dynamic performance test than BK3 test. The above-improved dynamic performance test can be applied to provide effective data for the research of modeling and error reduction of five-axis machine tools.

T-Spline Surface Toolpath Generation Using Watershed-Based Feature Recognition

The freeform surface is treated as a single machining region for most traditional toolpath generation algorithms. However, due to the complexity of a freeform surface, it is impossible to produce a high-quality surface using one unique machining process. Hence, region-based methods are widely investigated for freeform surface machining to achieve an optimized toolpath. The Non-Uniform Rational B-spline Surface (NURBS) represented freeform surface is not suitable for region-based toolpath generation because of the surface gaps caused by NURBS trimming and merging operations. To solve the limitation of the NURBS, T-spline is proposed with the advantages of being gap-free, having less control points, and local refinement, which is an ideal tool for region-based toolpath generation. Thus, T-spline is introduced to represent a freeform surface for its toolpath generation in the paper. A region-based toolpath generation method for the T-spline surface is proposed based on watershed technology. Firstly, watershed-based feature recognition is presented to divide the T-spline surface into a set of sub-regions. Secondly, the concept of a PolyBoundingBox that consists of a set of minimum bounding boxes is proposed to describe the sub-regions, and Manufacturing-Suitable Regions are constructed with the help of T-spline local refinement and the PolyBoundingBox. In the end, an optimized multi-rectangles toolpath generation algorithm is applied for sub-regions. The proposed method is tested using three synthetic T-spline surfaces, and the comparison results show the advantage in toolpath length and toolpath reversing number.

A tool path generation method for quasi-intermittent vibration assisted swing cutting

During the machining of freeform surfaces, the tool path will directly affect the machining accuracy of the surface, the execution of each axis of the machine tool, and the machining efficiency. Therefore, tool path planning is a very critical link in all types of diamond turning processes. In this paper, a new tool path generation strategy is proposed for machining freeform surfaces by quasi-intermittent vibration assisted swing cutting (QVASC) method. Due to the unique tool swing motion law of QVASC, the effective central angle of tool nose arc participating in the cutting is a parameter that is ignored by traditional cutting and is considered. This makes the generation of tool trajectories, tool geometry selection and freeform surfaces very different from traditional diamond cutting. According to the principle of QVASC, the tool parameters are analysed, and the tool position is designed in the cylindrical coordinate system. Interpolation was then performed by the Hermite spline interpolation theorem. The application of this strategy is discussed, and the sinusoidal surface, sinusoidal mesh surface and toric surface are taken as examples to simulate. The simulation succeeded in obtaining the tool path corresponding to the three curved surfaces processed by the QVASC method. The results prove that the tool trajectory generation strategy proposed in this paper is feasible. The proposed tool path generation strategy can provide a new reference for future freeform surfaces processing.

Study on a 2D field-based multi-objective tool-axis optimization algorithm based on covariant field theory for five-axis tool path generation

In five-axis machining, drastic change of tool axis has negative effects on machining efficiency and quality. Our published work proposed a unified mathematical framework to generate smooth tool-axis field and implemented in 1D domain (Yan et al., J Manuf Syst 48:30–37, 2018). In this paper, we extend the mathematical framework to 2D domain and the framework is an integral functional problem converting diverse machining requirements, such as gouge and collision free, smoothness, into mathematical expressions. A tool-axis vector field (TAVF) defined on the freeform surface is calculated by optimizing the integral functional problem. The surface is discrete into triangular mesh, and the discrete TAVF calculation problem is solved by a numeric 2D finite element method (FEM). Subsequently, the proposed algorithm is implemented to generate field-generated tool path (FGTP). The tool path has been used in machining hub of blade disk (blisk). The blisk is a complex workpiece that impellers should be gouge avoided. Machining experiments indicate that tool path generated by the proposed algorithm can avoid collision and improve smoothness on the whole surface. The freeform surface machining quality is highly improved compared with that machined by region-partitioned tool path (RPTP).

Automatic minimal partitioning method guaranteeing machining efficiency of free-form surfaces using a toroidal tool

Toolpath planning to machine free-form surfaces on a 3-axis CNC machine remains a complex issue. Research work has proven the relative effectiveness of toroidal tools in material removal rates as compared with spherical tools. However, this efficiency has only been confirmed and maximised for a specific feed direction, i.e. the one with the steepest slope. Since the optimal direction for the use of toroidal tools varies on the surface to be machined, more recent works have proposed surface partitioning methods where the surface to be machined is divided into zones, each machined in an optimal direction. The planning of machining toolpaths for free-form surfaces nowadays involves choosing the number of zones when cutting the surface to be machined: too coarse a partitioning will not guarantee the efficiency of using a toroidal tool, while too fine a partitioning will lead to increased travel times between the zones and frequent changes in direction, impairing productivity. The present article therefore proposes a minimum partitioning method for free-form surfaces guaranteeing the efficiency of a toroidal tool. A first section recalls the state of the art in the matter and the issues involved. The next section introduces the parameters needed to define a strategy. In the third section, an efficiency coefficient to quantify the benefits of using a toroidal tool is introduced. The fourth section describes a surface cutting strategy to ensure the efficiency of the tool at any point machined. The fifth section is dedicated to validating the results on machined and simulated parts in different configurations. Analysis of the results confirms the benefits of this new method.

Influence mechanism of machining angles on force induced error and their selection in five axis bullnose end milling

In the machining of complicated surfaces, the cutters with large length/diameter ratios are used widely and the deformation of the machining system is one of the principal error sources. During the process planning stage, the cutting direction angle, the cutter lead and tilt angles are usually optimized to minimize the force induced error. It may lead to a low machining efficiency for bullnose end mills, as the material removal rates are different largely for different machining angles. In this paper, the influence mechanism of the machining angles on the force induced error is studied based on the models of the instantaneous cutting force when the cutter flute traveling through the cutting contact point and the stiffness of the machining system. In order to evaluate the machining angles, the force induced error/efficiency indicator (FEI) is defined as the division of the force induced error and the equal volume sphere of the removed material. FEI is dimensionless, with the lower FEI, the lower force induced error and the higher machining efficiency. For optimal selection of the machining angles, the critical FEI is calculated with the constraint of force induced error and the desired material removal rate, and the critical FEI separate the set of the machining angles into two subsets. After the feed rate scheduling process, the machining angles in the optimal subset would have higher machining accuracy and efficiency, while the machining angles in the other subset have lower machining accuracy and efficiency. Through the machining experiment of five axis machining and freeform surface machining, the effectiveness and superiority of the proposed FEI method is verified with a bullnose end mill, which can improve the machining efficiency with the constraint of force induced error.

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

Abstract 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.

Tool wear analysis of ball nose end mill in the finish machining of free form surfaces

The present study investigates the cutting performance of ball nose end mills in high-speed dry-milling of a specific mold steel grade Super Plast ® 300 (SP300). The cutting performance was evaluated in terms of cutting length and tool wear. However, the milling tests were performed at finishing cutting conditions with a two fluted solid carbide ball nose end mill (diameter d is 16 mm, TiCN coating). Nevertheless, this investigation focuses mainly on the flank wear of ball nose end mill. It was found from the results that, the dominant wear mechanism was abrasive wear. Further, the flanks wear increases brutally at a specific cutting length or time. This is made when the coating layer vanished.

Surface topography analysis of ball end milled tool steel surfaces

Many mechanical components require mirror–like surface appearance. When the application concerns the manufacturing of steel dies and moulds, material removal processes are the preferential choice in order to achieve the wanted dimensions and surface topography. In particular, ball milling is used in all those cases that require the machining of free form surfaces. When mirror-like surface appearance is in focus in such components, the final machining operations consists in a very shallow cut. The theoretical surface roughness (kinematic surface topography) that can be achieved in a finishing operation by ball end milling is orders of magnitude below the actual surface roughness. Beside runout and machine tool positioning errors, the quality of the cutting tools is a key factor in determining the surface topography. The combination of shallow depth of cut together with the finite size of the cutting edge radius of the tool are responsible for the occurrence of material smearing phenomena. Smearing, consisting in the accumulation of plastically deformed material over the surface, is particularly detrimental for the aesthetic functionality of machined components because it is responsible of the “foggy” appearance. In order to minimize the occurrence of the smeared material it is necessary to have a good understanding of the causes of the smearing formation process. The aim of this paper is the description and quantification of the smearing phenomena for ball end milling operations. The location of the smeared material is determined through SEM image analysis and related with the direction of the cutting speed and milling strategy. Subsequently the volume of the smeared material is quantified through a combination of confocal microscopy and SEM image analysis. Based on the volumetric analysis of the smeared material a new method for determining the Minimum Uncut Chip Thickness for the material is proposed.

The Effect of the Feed Direction on the Micro- and Macro Accuracy of 3D Ball-end Milling of Chromium-Molybdenum Alloy Steel.

The machining of free form surfaces is one of the most challenging problems in the field of metal cutting technology. The produced part and machining process should satisfy the working, accuracy, and financial requirements. The accuracy can describe dimensional, geometrical, and surface roughness parameters. In the current article, three of them are investigated in the case of the ball-end milling of a convex and concave cylindrical surface form 42CrMo4 steel alloy. The effect of the tool path direction is investigated and the other cutting parameters are constant. The surface roughness and the geometric error are measured by contact methods. Based on the results, the surface roughness, dimensional error, and the geometrical error mean different aspects of the accuracy, but they are not independent from each other. The investigated input parameters have a similar effect on them. The regression analyses result a very good liner regression for geometric errors and shows the importance of surface roughness.

Generation and characterization of ultra-precision compound freeform surfaces.

Compound freeform surfaces are widely used in bionic and optical applications. The manufacturing and measurement of such surfaces are challenging due to the complex geometry with multi-scale features in a high precision level with sub-micrometer form accuracy and nanometer surface finish. This article presents a study of ultra-precision machining and characterization of compound freeform surfaces. A hybrid machining process by combining slow slide servo and fast tool servo is proposed to machine compound freeform surfaces. The machining process for this hybrid tool servo is explained, and tool path generation is presented. Then, a normal template-based matching and characterization method is proposed to evaluate such compound freeform surfaces. Experimental studies are undertaken to machine a compound freeform surface using the proposed method based on a four-axis ultra-precision machine tool. The machined compound freeform surface is also measured and characterized by the proposed analysis and characterization method. The experimental results are presented, and the machining errors for compound freeform surfaces are also discussed.