Selection of master cutter paths in sculptured surface machining by employing curvature principle

In the Isoscallop strategy of sculptured surface machining, one of the surface edges is generally chosen as the Master Cutter Path (MCP)—from which other cutter paths are derived such that the roughness produced is uniform. In this paper, the MCPs have been chosen from the maximum or minimum curvature loci of the surface. Those loci that divide the surface into distinct zones of similar curvature are adopted as MCPs. Secondary cutter path generation is carried out employing standard isoscallop formulation and problems associated with multiple MCPs have been identified and addressed. MCPs along the locus of maximum convex curvature lead to a considerable reduction in machining time while those for minimum curvature (maximum flatness) yield a reduction in CL data file size.     

Optimum orientation of a torus milling cutter: Method to balance the transversal cutting force

In this paper, a new method for tool positioning in milling on torus cutters with round inserts is presented. A new criterion associated with balancing of the transversal cutting force is used to compute a tool orientation. The considered tool inclination is towards the back of the tool. In this case, all inserts work simultaneously and generate a continuous cutting phenomenon. Each of the inserts produces a transversal cutting force; some being positive while others are negative. A small tool axis inclination angle leads to balancing the transversal cutting force exerted on the tool and then reducing deflection and vibrations in milling operations. Firstly, this approach to the dynamic aspects relating to cutting forces in the milling process is significant for mould and die manufacturing since it allows polishing time to be reduced. In addition, as vibrations are reduced, enhanced surface quality can be obtained directly on free-form surfaces such as aeronautic fittings.     

Penetration–elimination method for five-axis CNC machining of sculptured surfaces

In this paper, a new tool positioning strategy for five-axis machining, called the penetration–elimination method (PEM), is introduced. The PEM gains from two innovative techniques that can considerably improve the computational efficiency during the calculation of the optimal tool orientations.The first technique includes developing a quantitative definition for the gouging concept and using this definition in conjunction with powerful numerical root-finder algorithms to determine the optimized tool orientations. The second technique dynamically detects the ineffective grid points and drops them from calculations and consequently takes a great role in reducing the computational burden. The ability of the PEM in removing various types of gouging has been shown via several examples. The computational efficiency of the PEM has been compared with another recently described method named the arc-intersect method (AIM). This comparison shows that although the two methods reach the same solution for the tool orientation, the PEM is averagely 7.5 times faster than the AIM.     

Improving machined surface textures in avoiding five-axis singularities considering tool orientation angle changes

This paper looks into the irregular machined surface textures appearing in the process of avoiding five-axis singularities using the C-space based tool orientation translation method. At first, the mechanism for the appearances of the irregular surface textures is analyzed. A cutting simulation in VERICUT reveals that irregular surface textures are actually caused by lacking control of the tool orientation angles in the orientation modification process. Realizing that, a modified particle swarm optimization (PSO) is intergraded into the previous tool orientation translation method. In the PSO, the particle evolving equations are redefined and a mutation operation is added. The objective of the PSO is to find an optimal translating vector in the C-space so that the changed tool orientation angles can reach minimum values. In this way, the surface textures can be controlled. Three comparative cutting experiments with fillet endmills are carried out to verify the effect of the proposed method. The experimental results show that: (1) with the tool orientation translation method, the five-axis singular problem can be well avoided; and (2) with the optimal translating vector found by the PSO, the machined surface textures can be greatly improved.     

The analysis of correlative error in principal axis method for five-axis machining of sculptured surfaces

Correlative error is a kind of error between the cutter locations. This text presents a detailed analysis about correlative error in the principal axis method (PAM) that is a strategy of tool positioning for five-axis machining. It points out all the strategies based on linear projection cannot avoid this interference and cannot be disregarded especially in the strategies with large stepover. Accurate calculating is made individually on linear and curve feed and formulae are developed. The author also gave the available application range of PAM and the algorithm for estimating correlative error.     

Bézier polygons for the linearization of dual NURBS curve in five-axis sculptured surface machining

Motivated by the excellent performance of three-axis NURBS interpolation, this paper presents a numerically efficient and accuracy controllable five-axis sculptured surface machining method with dual NURBS curve. Unlike the traditional three-axis NURBS interpolation, a dual NURBS format of the five-axis toolpath is developed to accurately and smoothly describe the tool movement in the part coordinate system. Different from the subdivision methods using the Taylor series expansion or inverse function, a piece-wise Bézier curve method is implemented to fast subdivide the NURBS curve within the user-defined tolerance. A generic rotation tool center point management module is also designed to realize the coordinate transformation and adaptive nonlinear error control for major five-axis machine tools. The overall effectiveness of the proposed five-axis NURBS machining scheme is demonstrated by the five-axis machining of an impeller’s flow channel.     

Swept surface determination for five-axis numerical control machining

This paper presents a closed-form solution of the swept profile of a generalized cutter in five-axis numerical control (NC) machining. The machine configurations and tool movements defined in NC programs are considered to model the true machine tool trajectory, which includes the linearly translational and rotational movements. Based on the machine tool trajectory and the cutter geometry, the cutter’s instantaneous swept profile is determined. By integrating the intermediate swept profiles, the cutter’s swept envelope can be constructed and applied to NC verification. The proposed method provides the explicit solution of the swept profile of a generalized cutter, which is important but not possible in the existing methods for five-axis NC verification. The computer implementations show that the approach developed is superior to the traditional methods.     

The influence of cutter orientation and workpiece angle on machinability when high-speed milling Inconel 718 under finishing conditions

The paper details results from a comprehensive series of experiments on the effects of key operating variables; cutter orientation and workpiece tilt angle, on tool life/length cut, cutting force, workpiece surface roughness (R_a), subsurface microstructure/microhardness and residual stress, when high-speed milling under finishing conditions. In terms of length cut, the 8 mm diameter coated (TiAlCrN multi-layer) carbide ball nose end mills achieved tool life values approaching 200 m. Life results for the horizontal downwards orientation when cutting with a workpiece tilt angle of 45° were similar to those when operating with the workpiece mounted horizontally, however, cutting forces were significantly higher in the latter case. Evidence of tool chatter was also observed from cutting force signatures with the horizontal upwards mode. Mean compressive surface residual stresses up to −850 MPa measured parallel to the feed direction were obtained when machining using worn tools with a 0° workpiece inclination, while tensile stresses were obtained when machining with horizontal downwards orientation.     

Enhanced virtual machining for sculptured surfaces by integrating machine tool error models into NC machining simulation

Sculptured surface machining is a time-consuming and costly process. It requires simultaneously controlled motion of the machine axes. However, positioning inaccuracies or errors exist in machine tools. The combination of error motions of the machine axes will result in a complicated pattern of part geometry errors. In order to quantitatively predict these part geometry errors, a new application framework ‘enhanced virtual machining’ is developed. It integrates machine tool error models into NC machining simulation. The ideal cutter path in the NC program for surface machining is discretized into sub-paths. For each interpolated cutter location, the machine geometric errors are predicted from the machine tool error model. Both the solid modeling approach and the surface modeling approach are used to translate machine geometric errors into part geometry errors for sculptured surface machining. The solid modeling approach obtains the final part geometry by subtracting the tool swept volume from the stock geometric model. The surface modeling approach approximates the actual cutter contact points by calculating the cutting tool motion and geometry. The simulation results show that the machine tool error model can be effectively integrated into sculptured surface machining to predict part geometry errors before the real cutting begins.     

Machining accuracy improvement in five-axis flank milling of ruled surfaces

The aim of this study is to develop a new adjustment method for improving machining accuracy of tool path in five-axis flank milling of ruled surfaces. This method considers interpolation sampling time of the five-axis machine tools controller in NC tool path planning. The actual interpolation position and orientation between G01 commands are estimated with the first differential approximation of Taylor expansion. The tool swept volume is modeled using the envelope surface and compared with the design surface to determine the deviation, which corresponds to the machining error induced by the linear interpolation. We propose a feedrate adjustment rule that automatically controls the tool motion at feedrate-sensitive corners based on a bisection method, thus limiting the maximum machining errors and improving the machining accuracy. Experimental cuts are conducted on different ruled surfaces to verify the effectiveness of the proposed method. The result shows that it can enhance the machining quality in five-axis flank milling in both simulation and practical operation.     

用圆柱铣刀加工带冠弯扭叶片

本文把微分几何中曲线与曲面之间的“切触”概念应用于叶片复杂曲面的数控加工，提出用圆柱铣刀的外圆在五坐标联动中加工小曲率曲面的最佳切触条件。     

Generation of a regularly aligned surface pattern and control of cutter marks array by patch division milling

In this paper, a patch division milling technique that can generate a geometric surface pattern by means of a ball-end mill on a surface is proposed. The finished surface is divided into many same-size small patch segments such as triangles, quadrilaterals, or hexagons. The whole inside area of each patch is machined along a helical tool path with a high feed rate. A geometric surface pattern is generated by the cutting edges of the ball-end mill within the patch area, and after the machining of a series of patches, the machined surface is covered with many patches. It is shown that the aligned state of the cutter marks array on the patch can be controlled by the cross-feed, the feed speed per tooth, the number of teeth and the side length of the patch. A simulator was also developed to predict the aligned state of the cutter marks array in the patch. Comparing the machining on the patch division milling between an inclined flat surface and a cylindrical surface, the regularly aligned surface pattern and cutter marks array were found to agree well with the simulation results. The objective of this research is to establish the cutting method of generating regularly aligned surface pattern on the complex-shaped workpiece efficiently. If the surface pattern on the complex-shaped workpiece could be formed only by the ball-end milling with a machining center, it will be a very effective tool for the machinery industry.     

A global cutter positioning method for multi-axis machining of sculptured surfaces

Traditional cutter positioning methods have defects of global errors and incomplete optimization. Because of using local differential geometry and focusing on the cutting contact point, these defects cannot be avoided and will deteriorate accuracy in precision machining. The authors presented the conception of actual cutting edge of a toroidal mill which was extended from cutting contact point, and pointed out its importance in programming. Instantaneous cutter position error (ICPE) was also investigated. A new global method based on the ICPE curve was presented. Taking the relationship between surface and cutter into consideration thoroughly, this global method shows many advantages which have been verified by simulation and cutting tests.     

Predicting surface roughness in machining: a review

The general manufacturing problem can be described as the achievement of a predefined product quality with given equipment, cost and time constraints. Unfortunately, for some quality characteristics of a product such as surface roughness it is hard to ensure that these requirements will be met. This paper aims at presenting the various methodologies and practices that are being employed for the prediction of surface roughness.The resulting benefits allow for the manufacturing process to become more productive and competitive and at the same time to reduce any re-processing of the machined workpiece so as to satisfy the technical specifications. Each approach with its advantages and disadvantages is outlined and the present and future trends are discussed. The approaches are classified into those based on machining theory, experimental investigation, designed experiments and artificial intelligence (AI).     

Real-time generation and control of cutter path for 5-axis CNC machining

This paper presents a new approach to real-time generation and control of the cutter path for 5-axis machining applications. The cutter path generation method comprises real-time algorithms for cutter-contact path interpolation, cutter offsetting, and coordinate conversion. In addition, a global feedback loop is closed by the CNC interpolator so as to augment the controlled accuracy in practical cutter path generation. An error compensation algorithm and a feedrate adaptation algorithm for the control loop are developed, respectively.     

Validation of volumetric error compensation for a five-axis machine using surface mismatch producing tests and on-machine touch probing

In order to validate volumetric error compensation methods for five-axis machine tools, the machining of test parts has been proposed. For such tests, a coordinate measuring machine (CMM) or other external measurement, outside of the machine tool, is required to measure the accuracy of the machined part. In this paper, a series of machining tests are proposed to validate a compensation strategy and compare the machining accuracy before and after the compensation using only on-machine measurements. The basis of the tests is to machine slots, each completed using two different rotary axes indexations of the CNC machine tool. Using directional derivatives of the volumetric errors, it is possible to verify that a surface mismatch is produced between the two halves of the same slot in the presence of specific machine geometric errors. The mismatch at the both sides of the slot, which materializes the machine volumetric errors is measured using touch probing by the erroneous machine itself and with high accuracy since the measurement of both slot halves can be conducted using a single set of rotary axes indexation and in a volumetric region of a few millimetres. The effect of a compensation strategy is then validated by comparing the surface mismatch value for compensated and uncompensated slots.     

Optimized tool path generation based on dynamic programming for five-axis flank milling of rule surface

This paper presents a computation scheme that generates optimized tool path for five-axis flank milling of ruled surface. Tool path planning is transformed into a matching problem between two point sets in 3D space, sampled from the boundary curves of the machined surface. Each connection in the matching corresponds to a possible tool position. Dynamic programming techniques are applied to obtain the optimal combination of tool positions with the objective function as machining error. The error estimation considers both the deviation induced by the cutter at discrete positions and the one between them. The path planning problem is thus solved in a systematic manner by formulizing it as a mathematical programming task. In addition, the scheme incorporates several optimization parameters that allow generating new patterns of tool motion. Implementation results obtained from simulation and experiment indicate that our method produces better machining quality. This work provides a concise but effective approach for machining error control in five-axis flank milling.     

An accurate,efficient envelope approach to modeling the geometric deviation of the machined surface for a specific five-axis CNC machine tool

Geometric deviation, defined as the difference between the nominal surface and the simulation model of the machined surface, is the fundamental concern of five-axis tool path planning. Since the machined surface is part of the cutter envelope surface generated by the cutter motion, it is necessary to calculate the envelope surface in order to obtain the geometric deviation. In the stage of tool path planning, current approaches calculate the cutter envelope surface by using the cutter motion along the given tool path. However, the cutter motion of practical machining on a specific five-axis CNC machine tool is different from the given tool path. Moreover, the computation is very challenging when the accurate cutter motion of practical machining is applied to calculate the envelope surface. To overcome these two problems, a geometric envelope approach with two major distinctions is proposed in this paper. First, the envelope surface of the cutter undergoing a general motion is efficiently obtained as a closed-form vector expression. Second, the accurate cutter motion, which is determined by machine kinematic and interpolation scheme in practical machining, can be easily applied to calculate the accurate envelope surface. With the envelope surface, the geometric deviation is calculated to estimate the overcut or undercut in five-axis milling. An example is given to demonstrate the validity of the proposed method.     

用标准圆柱立铣刀加工成形圆柱螺旋曲面机理的研究

本文针对成形圆柱螺旋曲面加工,分析了以前加工方法存在的问题,提出一种新的加工方法-利用标准圆柱立铣刀来加工,该方法具有柔性好、成本低、效率高的优点。文中运用微分几何等理论,详细分析并建立了该加工方法的数学模型,得到了标准圆柱立铣刀直径及其安装角度的寻优方法。     

An improved method for scheduling the tool paths for three-axis surface machining

This paper presents a new tool-path scheduling method to improve the accuracy and efficiency of three-axis surface machining. The features of the proposed method include: (1) surface-error-based segmentation in the feed-forward direction; (2) consideration for the coupled effect of the segmentation in the feed-forward and the path-interval directions; and (3) compensation for the tool location to control the surface error and the segmentation efficiency. In this paper, we consider a ball-end mill for surface machining.