A cutting-tool-dependent approach for partitioning of sculptured surface

Topic of the paper is in the area of sculptured surface machining (SSM). The objectives of the paper are as follow. Firstly, to develop an approach that enables one detecting regions of sculptured surface those are not accessible for a cutting tool of a given design (i.e. regions, which cutter cannot reach without being obstructed by another portion of the part). Secondly, if we observe any not-machinable regions, the approach to be developed has enable one to subdivide the sculptured surface P onto the cutter-accessible and onto the cutter-not-accessible regions. To resolve the problem of sculptured surface partitioning, focal surfaces for the surfaces P and T were applied. Based on implementation of focal surfaces, cutting-tool-dependent characteristic surfaces are introduced. This enables derivation of equation for boundary curve, and enhancing the developed approach for locally extremal kinds of tangency of the surfaces P and T. The effectiveness of the proposed approach is verified from numerical simulation with the simple and clear examples. The main advantage of the developed approach over existing methods is that it incorporates topology not only of sculptured surface to be machined but also topology of the machining surface of a tool to be applied. This makes obtained results more fitted for engineering application. Taken as a whole, the topic covered in this paper enables one to develop reliable software for machining the sculptured surface on multi-axis CNC machine.     

A machining potential field approach to tool path generation for multi-axis sculptured surface machining

This paper presents a machining potential field (MPF) method to generate tool paths for multi-axis sculptured surface machining. A machining potential field is constructed by considering both the part geometry and the cutter geometry to represent the machining-oriented information on the part surface for machining planning. The largest feasible machining strip width and the optimal cutting direction at a surface point can be found on the constructed machining potential field. The tool paths can be generated by following the optimal cutting direction. Compared to the traditional iso-parametric and iso-planar path generation methods, the generated MPF multi-axis tool paths can achieve better surface finish with shorter machining time. Feasible cutter sizes and cutter orientations can also be determined by using the MPF method. The developed techniques can be used to automate the multi-axis tool path generation and to improve the machining efficiency of sculptured surface machining.     

Estimation of NC machining time using NC block distribution for sculptured surface machining

The estimation of NC machining time is of importance because it provides manufacturing engineers with information to accurately predict the productivity of an NC machine, as well as its production schedule. NC programs contain various machining information, such as tool positions, feed and speed rates, and other machine instructions. Nominal NC machining time can easily be obtained based on the NC program data. Actual machining time, however, cannot simply be found due to the dynamic characteristics of a NC machine controller, such as acceleration and deceleration effect. Hence, this study presents an NC machine time estimation model for machining sculptured surfaces, considering such dynamic characteristics of the machine. The proposed estimation model uses several factors, such as the distribution of NC blocks, angle between the blocks, federates, acceleration and deceleration constants, classifying tool feed rate patterns into four types based on the acceleration and deceleration profile, NC block length, and minimum feed rate. However, there exists an error for the actual machining time due to the lack of the measurement equipment or tools to gauge an exact minimum feed rate. Thus, this paper proposes a machining time estimation model using NC block distributions, lowering down the error caused by the inaccurate minimum feed rate. The proposed machining time estimator performs at around 10% of mean error.     

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.     

Automated surface subdivision and tool path generation for -axis CNC machining of sculptured parts

As an innovative and cost-effective method for carrying out multiple-axis CNC machining, -axis CNC machining technique adds an automatic indexing/rotary table with two additional discrete rotations to a regular 3-axis CNC machine, to improve its ability and efficiency for machining complex sculptured parts. In this work, a new tool path generation method to automatically subdivide a complex sculptured surface into a number of easy-to-machine surface patches; identify the favorable machining set-up/orientation for each patch; and generate effective 3-axis CNC tool paths for each patch is introduced. The method and its advantages are illustrated using an example of sculptured surface machining. The work contributes to automated multiple-axis CNC tool path generation for sculptured part machining and forms a foundation for further research.     

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.     

An intelligent approach for the prediction of surface roughness in ball-end machining of polypropylene

Manufacturing paradigms over the last 150 years have changed from craft production, to mass production and now to mass customisation. One further extension of mass customisation is personalised manufacture, which is the concept of providing bespoke products to the individual consumer. As a result this has brought about the need for a greater degree of sophistication in manufacturing practises and the technologies employed. This bespoke form of manufacture of consumer goods is now being pursued on CNC machining centres as opposed to the alternative of highly expensive rapid prototyping methods. The problem with this form of manufacture is that the products are generally free formed objects which require sophisticated setups and machining. Ball-end machining is a method used to create cusp-type geometry, which is employed on CNC machines to create sculptured surfaces. The objective of this research is to provide a predictive model using a design of experiments strategy to obtain optimised machining parameters for a specific surface roughness in ball-end machining of polypropylene. This paper reports on new manufacturing knowledge to machine polypropylene using ball-end tooling in order to generate personalised sculptured surface products.     

Iso-planar interpolation for the machining of implicit surfaces

The paper presents an approach for on-line path generation and interpolation for the machining of implicit surfaces. For a given implicit surface, once the cutting plane direction and cut-in points have been selected, iso-planar tool paths and interpolated points can be calculated on-line according to the feedrate and scallop height requirements. The approach enables the tool position and orientation to be correctly calculated at each interpolated point. Validation examples are provided for the interpolation of cyclide surfaces with planar and curved boundaries.     

Maximal intersection of spherical polygons by an arc with applications to 4-axis machining

Many geometric optimization problems in CAD/CAM can be reduced to a maximal intersection problem on the sphere: given a set of N simple spherical polygons on the unit sphere and a real number constant L≤2π, find an arc of length L on the unit sphere that intersects as many spherical polygons as possible. Past results can only solve this maximization problem for two very restricted special cases: the arc must be either a great circle or a semi-great circle. In this paper, a simple and deterministic algorithm based on domain partitioning is presented for solving this maximal arc intersection problem in the general case when the number L is arbitrary. The algorithm is made possible by reducing the domain of the arcs to a continuous sub-space in R² and then establishing a quotient space partitioning in this sub-space based on a congruence relation. The number of the constituting congruent sub-regions in this quotient space partitioning is shown to have an upper-bound O(E³), where E is the total number of edges on the polygons. The proposed algorithm has a worst-case upper bound O(ME) on its running time, where M is an output-sensitive number and is bounded by O(E³). Examples including two realistic tests for 4-axis NC machining are presented.     

Second order approximation of tool envelope surface for 5-axis machining with single point contact

For 5-axis machining with single point contact, this paper proposes a method to calculate second order approximation of the tool envelope surface by using only one tool position. As we known, the true machining errors are deviations between designed surface and tool envelope surface. But it is impossible to determine the whole shape of the tool envelope surface before all tool positions are obtained. Hence, it is difficult to position the tool individually and consider true errors at the same time. Basic Curvature Equations of Locally Tool Positioning (BCELTP) are presented to solve this problem in some degree. By using them under some special conditions, given one tool position, the local shape (second order approximation) of the tool envelope surface can be calculated precisely at the corresponding cutter contact point. These equations make it convenient to adjust the tool position individually until true errors are reduced in some degree. So, they are useful for optimizing tool positions locally. Finally, some examples are given to verify the correctness and practicability of theory.     

A new approach to z-level contour machining of triangulated surface models using fillet endmills

Precision z-level contour machining is important for various computer-aided manufacturing (CAM) applications such as pocket machining and high-speed machining (HSM). This paper presents a new z-level contour tool-path generation algorithm for NC machining of triangulated surface models. Traditional approaches of z-level machining rely on the creation of accurate CL (cutter location) surfaces by surface offsetting or high-density z-map generation, which is computationally expensive and memory demanding. In contrast, this paper presents a novel approach to the generation of CL data directly from the section polygon of a triangulated surface model. For each polygon vertex of the contour, the offset direction is determined by the normal to the edge, while the offset distance is not fixed but is determined from the cutter shape and the part surface. An interference-free tool-path computation algorithm using fillet endmills is developed. Since there is no need to create a complete CL surface or high-density z-map grids, this proposed method is highly efficient and more flexible, and can be directly applied to triangulated surfaces either tessellated from CAD models, or reconstructed from 3D scanned data for reverse engineering (RE) applications.     

Three dimensional thermal finite element simulation of electro-discharge diamond surface grinding

The key to achieve good surface integrity in the workpiece due to Electro-Discharge Diamond Grinding (EDDG) process, which is hybrid of grinding and EDM, is by preventing the excessive temperature and thermal stress generated during the process. EDDG in surface grinding mode called Electro-Discharge Diamond Surface Grinding (EDDSG), used for finishing operation, is a complex machining process where several disciplines of science and engineering are involved in its theory. The complexity of the process includes the random occurrence of spark during EDM process and nonlinear behavior of workpiece material includes temperature dependent thermal properties. The present work involves the development of a simulation model to simulate the complex EDDSG process which consists of simulation of each constituent process namely EDM and surface grinding for temperature and thermal stress distribution. In order to simulate the realistic complex conditions, the three dimensional FEM is used in the process of development of the model accounting the random occurrence of the spark during EDM. The effect of different dielectric fluid, duty factor and energy partition during EDM on the temperature distribution and MRR study related to EDM contribution are reported. It is observed that the spark contributes primarily to the temperature. The predicted results can be used to determine the surface integrity of the machined surface.     

Comparison of impervious surface area and normalized difference vegetation index as indicators of surface urban heat island effects in Landsat imagery

This paper compares the normalized difference vegetation index (NDVI) and percent impervious surface as indicators of surface urban heat island effects in Landsat imagery by investigating the relationships between the land surface temperature (LST), percent impervious surface area (%ISA), and the NDVI. Landsat Thematic Mapper (TM) and Enhanced Thematic Mapper Plus (ETM+) data were used to estimate the LST from four different seasons for the Twin Cities, Minnesota, metropolitan area. A map of percent impervious surface with a standard error of 7.95% was generated using a normalized spectral mixture analysis of July 2002 Landsat TM imagery. Our analysis indicates there is a strong linear relationship between LST and percent impervious surface for all seasons, whereas the relationship between LST and NDVI is much less strong and varies by season. This result suggests percent impervious surface provides a complementary metric to the traditionally applied NDVI for analyzing LST quantitatively over the seasons for surface urban heat island studies using thermal infrared remote sensing in an urbanized environment.